{"instruction": "Find an antiderivative of -594*log(12*x + 18)*sin(11*x + 12) + 648*cos(11*x + 12)/(12*x + 18) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 54*log(12*x + 18)*cos(11*x + 12)", "id": "calculus-L2-a365990bfc2dd90e38c6", "source_id": "calculus-a365990bfc2dd90e38c6", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -594*log(12*x + 18)*sin(11*x + 12) + 648*cos(11*x + 12)/(12*x + 18) with respect to x.", "answer": "54*log(12*x + 18)*cos(11*x + 12)", "expr": "-594*log(12*x + 18)*sin(11*x + 12) + 648*cos(11*x + 12)/(12*x + 18)", "primitive": "54*log(12*x + 18)*cos(11*x + 12)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 14*(20*exp(3*x) + 11)*sin(x + 18) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 14*(20*exp(3*x) + 11)*cos(x + 18) + 840*exp(3*x)*sin(x + 18)", "id": "calculus-L2-78306a852ae200c95cf7", "source_id": "calculus-78306a852ae200c95cf7", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 14*(20*exp(3*x) + 11)*sin(x + 18) with respect to x.", "answer": "14*(20*exp(3*x) + 11)*cos(x + 18) + 840*exp(3*x)*sin(x + 18)", "expr": "14*(20*exp(3*x) + 11)*sin(x + 18)", "primitive": "14*(20*exp(3*x) + 11)*sin(x + 18)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = sin(3*x)*cos(11*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -11*sin(3*x)*sin(11*x) + 3*cos(3*x)*cos(11*x)", "id": "calculus-L2-cebdb4e7f215bcd7656f", "source_id": "calculus-cebdb4e7f215bcd7656f", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = sin(3*x)*cos(11*x) with respect to x.", "answer": "-11*sin(3*x)*sin(11*x) + 3*cos(3*x)*cos(11*x)", "expr": "sin(3*x)*cos(11*x)", "primitive": "sin(3*x)*cos(11*x)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -4*sin(4*x)**2 + 4*cos(4*x)**2 with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: sin(4*x)*cos(4*x)", "id": "calculus-L2-75741170043f0f750334", "source_id": "calculus-75741170043f0f750334", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -4*sin(4*x)**2 + 4*cos(4*x)**2 with respect to x.", "answer": "sin(4*x)*cos(4*x)", "expr": "-4*sin(4*x)**2 + 4*cos(4*x)**2", "primitive": "sin(4*x)*cos(4*x)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 112*x*exp(8*x**2 + 15) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 7*exp(8*x**2 + 15)", "id": "calculus-L2-8810b1c772757aae0f03", "source_id": "calculus-8810b1c772757aae0f03", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 112*x*exp(8*x**2 + 15) with respect to x.", "answer": "7*exp(8*x**2 + 15)", "expr": "112*x*exp(8*x**2 + 15)", "primitive": "7*exp(8*x**2 + 15)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 3128*log(6*x + 16)/(8*x + 11) + 2346*log(8*x + 11)/(6*x + 16) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 391*log(6*x + 16)*log(8*x + 11)", "id": "calculus-L2-6c02e3c72c374640d18b", "source_id": "calculus-6c02e3c72c374640d18b", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 3128*log(6*x + 16)/(8*x + 11) + 2346*log(8*x + 11)/(6*x + 16) with respect to x.", "answer": "391*log(6*x + 16)*log(8*x + 11)", "expr": "3128*log(6*x + 16)/(8*x + 11) + 2346*log(8*x + 11)/(6*x + 16)", "primitive": "391*log(6*x + 16)*log(8*x + 11)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 17*exp(3*x**2 + 10) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 102*x*exp(3*x**2 + 10)", "id": "calculus-L2-f307e096a6ef94efd0c1", "source_id": "calculus-f307e096a6ef94efd0c1", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 17*exp(3*x**2 + 10) with respect to x.", "answer": "102*x*exp(3*x**2 + 10)", "expr": "17*exp(3*x**2 + 10)", "primitive": "17*exp(3*x**2 + 10)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 437*cos(3*x + 16)*cos(6*x + 14) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -1311*sin(3*x + 16)*cos(6*x + 14) - 2622*sin(6*x + 14)*cos(3*x + 16)", "id": "calculus-L2-ce4643d176b85bfa327b", "source_id": "calculus-ce4643d176b85bfa327b", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 437*cos(3*x + 16)*cos(6*x + 14) with respect to x.", "answer": "-1311*sin(3*x + 16)*cos(6*x + 14) - 2622*sin(6*x + 14)*cos(3*x + 16)", "expr": "437*cos(3*x + 16)*cos(6*x + 14)", "primitive": "437*cos(3*x + 16)*cos(6*x + 14)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of (-32*x**3 - 15*x**2 + 16*x - 7)*(-3*x**4 + 6*x**3 - 8*x**2 + x + 5) + (-12*x**3 + 18*x**2 - 16*x + 1)*(-8*x**4 - 5*x**3 + 8*x**2 - 7*x + 1) with respect to x from 1 to 2. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 3736", "id": "calculus-L2-708740b3082673606a9f", "source_id": "calculus-708740b3082673606a9f", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of (-32*x**3 - 15*x**2 + 16*x - 7)*(-3*x**4 + 6*x**3 - 8*x**2 + x + 5) + (-12*x**3 + 18*x**2 - 16*x + 1)*(-8*x**4 - 5*x**3 + 8*x**2 - 7*x + 1) with respect to x from 1 to 2.", "answer": "3736", "expr": "(-32*x**3 - 15*x**2 + 16*x - 7)*(-3*x**4 + 6*x**3 - 8*x**2 + x + 5) + (-12*x**3 + 18*x**2 - 16*x + 1)*(-8*x**4 - 5*x**3 + 8*x**2 - 7*x + 1)", "primitive": "(-8*x**4 - 5*x**3 + 8*x**2 - 7*x + 1)*(-3*x**4 + 6*x**3 - 8*x**2 + x + 5)", "lower": "1", "upper": "2", "split": "dev"}
{"instruction": "Find an antiderivative of 320*exp(8*x)*log(9*x + 24) + 18*(20*exp(8*x) + 8)/(9*x + 24) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 2*(20*exp(8*x) + 8)*log(9*x + 24)", "id": "calculus-L2-060b81c01def4472d6d5", "source_id": "calculus-060b81c01def4472d6d5", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 320*exp(8*x)*log(9*x + 24) + 18*(20*exp(8*x) + 8)/(9*x + 24) with respect to x.", "answer": "2*(20*exp(8*x) + 8)*log(9*x + 24)", "expr": "320*exp(8*x)*log(9*x + 24) + 18*(20*exp(8*x) + 8)/(9*x + 24)", "primitive": "2*(20*exp(8*x) + 8)*log(9*x + 24)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (3*x**2 - 9*x - 3)/(x**2 + 7) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(3*x**2 - 9*x - 3)/(x**2 + 7)**2 + (6*x - 9)/(x**2 + 7)", "id": "calculus-L2-1c9b04fe131e5b87ce24", "source_id": "calculus-1c9b04fe131e5b87ce24", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (3*x**2 - 9*x - 3)/(x**2 + 7) with respect to x.", "answer": "-2*x*(3*x**2 - 9*x - 3)/(x**2 + 7)**2 + (6*x - 9)/(x**2 + 7)", "expr": "(3*x**2 - 9*x - 3)/(x**2 + 7)", "primitive": "(3*x**2 - 9*x - 3)/(x**2 + 7)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(7 - 3*x)/(x**2 + 15)**2 - 3/(x**2 + 15) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (7 - 3*x)/(x**2 + 15)", "id": "calculus-L2-d12648edff22b43c33da", "source_id": "calculus-d12648edff22b43c33da", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(7 - 3*x)/(x**2 + 15)**2 - 3/(x**2 + 15) with respect to x.", "answer": "(7 - 3*x)/(x**2 + 15)", "expr": "-2*x*(7 - 3*x)/(x**2 + 15)**2 - 3/(x**2 + 15)", "primitive": "(7 - 3*x)/(x**2 + 15)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 27*(6*exp(10*x) + 12)*sin(9*x + 21) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 243*(6*exp(10*x) + 12)*cos(9*x + 21) + 1620*exp(10*x)*sin(9*x + 21)", "id": "calculus-L2-e9857a80dbaf68997d6c", "source_id": "calculus-e9857a80dbaf68997d6c", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 27*(6*exp(10*x) + 12)*sin(9*x + 21) with respect to x.", "answer": "243*(6*exp(10*x) + 12)*cos(9*x + 21) + 1620*exp(10*x)*sin(9*x + 21)", "expr": "27*(6*exp(10*x) + 12)*sin(9*x + 21)", "primitive": "27*(6*exp(10*x) + 12)*sin(9*x + 21)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (7 - 5*x)/(x**2 + 8) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(7 - 5*x)/(x**2 + 8)**2 - 5/(x**2 + 8)", "id": "calculus-L2-c3adb07d3db8398c784f", "source_id": "calculus-c3adb07d3db8398c784f", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (7 - 5*x)/(x**2 + 8) with respect to x.", "answer": "-2*x*(7 - 5*x)/(x**2 + 8)**2 - 5/(x**2 + 8)", "expr": "(7 - 5*x)/(x**2 + 8)", "primitive": "(7 - 5*x)/(x**2 + 8)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 725*log(x + 3)*sin(3*x + 12) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 2175*log(x + 3)*cos(3*x + 12) + 725*sin(3*x + 12)/(x + 3)", "id": "calculus-L2-aae5fe7c2711312dc19c", "source_id": "calculus-aae5fe7c2711312dc19c", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 725*log(x + 3)*sin(3*x + 12) with respect to x.", "answer": "2175*log(x + 3)*cos(3*x + 12) + 725*sin(3*x + 12)/(x + 3)", "expr": "725*log(x + 3)*sin(3*x + 12)", "primitive": "725*log(x + 3)*sin(3*x + 12)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of 14*(8*x + 8)*log(12*x + 1) + 168*(4*x**2 + 8*x + 1)/(12*x + 1) with respect to x from 1 to 2. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -182*log(13) + 462*log(25)", "id": "calculus-L2-f7def8fcf7977db057de", "source_id": "calculus-f7def8fcf7977db057de", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of 14*(8*x + 8)*log(12*x + 1) + 168*(4*x**2 + 8*x + 1)/(12*x + 1) with respect to x from 1 to 2.", "answer": "-182*log(13) + 462*log(25)", "expr": "14*(8*x + 8)*log(12*x + 1) + 168*(4*x**2 + 8*x + 1)/(12*x + 1)", "primitive": "14*(4*x**2 + 8*x + 1)*log(12*x + 1)", "lower": "1", "upper": "2", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (-3*x**2 + x)/(x**2 + 4) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(-3*x**2 + x)/(x**2 + 4)**2 + (1 - 6*x)/(x**2 + 4)", "id": "calculus-L2-9bcc691d1e0b6a524dd0", "source_id": "calculus-9bcc691d1e0b6a524dd0", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (-3*x**2 + x)/(x**2 + 4) with respect to x.", "answer": "-2*x*(-3*x**2 + x)/(x**2 + 4)**2 + (1 - 6*x)/(x**2 + 4)", "expr": "(-3*x**2 + x)/(x**2 + 4)", "primitive": "(-3*x**2 + x)/(x**2 + 4)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 4312*log(9*x + 19)*cos(7*x + 29) + 5544*sin(7*x + 29)/(9*x + 19) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 616*log(9*x + 19)*sin(7*x + 29)", "id": "calculus-L2-e411208f517560acee94", "source_id": "calculus-e411208f517560acee94", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 4312*log(9*x + 19)*cos(7*x + 29) + 5544*sin(7*x + 29)/(9*x + 19) with respect to x.", "answer": "616*log(9*x + 19)*sin(7*x + 29)", "expr": "4312*log(9*x + 19)*cos(7*x + 29) + 5544*sin(7*x + 29)/(9*x + 19)", "primitive": "616*log(9*x + 19)*sin(7*x + 29)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 84*sin(12*x + 22)*cos(3*x + 7) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -252*sin(3*x + 7)*sin(12*x + 22) + 1008*cos(3*x + 7)*cos(12*x + 22)", "id": "calculus-L2-c695f9159bc23e534e84", "source_id": "calculus-c695f9159bc23e534e84", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 84*sin(12*x + 22)*cos(3*x + 7) with respect to x.", "answer": "-252*sin(3*x + 7)*sin(12*x + 22) + 1008*cos(3*x + 7)*cos(12*x + 22)", "expr": "84*sin(12*x + 22)*cos(3*x + 7)", "primitive": "84*sin(12*x + 22)*cos(3*x + 7)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 13*(x**4 + 4*x**3 + 3*x - 7)*sin(11*x + 5) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 13*(4*x**3 + 12*x**2 + 3)*sin(11*x + 5) + 143*(x**4 + 4*x**3 + 3*x - 7)*cos(11*x + 5)", "id": "calculus-L2-73bc0670403e74b21af3", "source_id": "calculus-73bc0670403e74b21af3", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 13*(x**4 + 4*x**3 + 3*x - 7)*sin(11*x + 5) with respect to x.", "answer": "13*(4*x**3 + 12*x**2 + 3)*sin(11*x + 5) + 143*(x**4 + 4*x**3 + 3*x - 7)*cos(11*x + 5)", "expr": "13*(x**4 + 4*x**3 + 3*x - 7)*sin(11*x + 5)", "primitive": "13*(x**4 + 4*x**3 + 3*x - 7)*sin(11*x + 5)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of 7*(-4*x**3 + 12*x**2 - 8*x + 4)*log(7*x + 22) + 49*(-x**4 + 4*x**3 - 4*x**2 + 4*x + 9)/(7*x + 22) with respect to x from 0 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -63*log(22) + 84*log(43)", "id": "calculus-L2-07124c7ee1b774378655", "source_id": "calculus-07124c7ee1b774378655", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of 7*(-4*x**3 + 12*x**2 - 8*x + 4)*log(7*x + 22) + 49*(-x**4 + 4*x**3 - 4*x**2 + 4*x + 9)/(7*x + 22) with respect to x from 0 to 3.", "answer": "-63*log(22) + 84*log(43)", "expr": "7*(-4*x**3 + 12*x**2 - 8*x + 4)*log(7*x + 22) + 49*(-x**4 + 4*x**3 - 4*x**2 + 4*x + 9)/(7*x + 22)", "primitive": "7*(-x**4 + 4*x**3 - 4*x**2 + 4*x + 9)*log(7*x + 22)", "lower": "0", "upper": "3", "split": "dev"}
{"instruction": "Find an antiderivative of 5589*log(4*x + 28)*cos(9*x + 27) + 2484*sin(9*x + 27)/(4*x + 28) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 621*log(4*x + 28)*sin(9*x + 27)", "id": "calculus-L2-68cc94c3e7e1360fe332", "source_id": "calculus-68cc94c3e7e1360fe332", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 5589*log(4*x + 28)*cos(9*x + 27) + 2484*sin(9*x + 27)/(4*x + 28) with respect to x.", "answer": "621*log(4*x + 28)*sin(9*x + 27)", "expr": "5589*log(4*x + 28)*cos(9*x + 27) + 2484*sin(9*x + 27)/(4*x + 28)", "primitive": "621*log(4*x + 28)*sin(9*x + 27)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(x**2 + 2*x + 7)/(x**2 + 5)**2 + (2*x + 2)/(x**2 + 5) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (x**2 + 2*x + 7)/(x**2 + 5)", "id": "calculus-L2-992c318b59ecc590ab3e", "source_id": "calculus-992c318b59ecc590ab3e", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(x**2 + 2*x + 7)/(x**2 + 5)**2 + (2*x + 2)/(x**2 + 5) with respect to x.", "answer": "(x**2 + 2*x + 7)/(x**2 + 5)", "expr": "-2*x*(x**2 + 2*x + 7)/(x**2 + 5)**2 + (2*x + 2)/(x**2 + 5)", "primitive": "(x**2 + 2*x + 7)/(x**2 + 5)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 351*log(4*x + 29)*cos(6*x + 24) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2106*log(4*x + 29)*sin(6*x + 24) + 1404*cos(6*x + 24)/(4*x + 29)", "id": "calculus-L2-f879dfc6ab234c033594", "source_id": "calculus-f879dfc6ab234c033594", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 351*log(4*x + 29)*cos(6*x + 24) with respect to x.", "answer": "-2106*log(4*x + 29)*sin(6*x + 24) + 1404*cos(6*x + 24)/(4*x + 29)", "expr": "351*log(4*x + 29)*cos(6*x + 24)", "primitive": "351*log(4*x + 29)*cos(6*x + 24)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = sin(2*x)*cos(19*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -19*sin(2*x)*sin(19*x) + 2*cos(2*x)*cos(19*x)", "id": "calculus-L2-e7bc49c1f92db16c7d6a", "source_id": "calculus-e7bc49c1f92db16c7d6a", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = sin(2*x)*cos(19*x) with respect to x.", "answer": "-19*sin(2*x)*sin(19*x) + 2*cos(2*x)*cos(19*x)", "expr": "sin(2*x)*cos(19*x)", "primitive": "sin(2*x)*cos(19*x)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(-7*x**2 - 3)/(x**2 + 10)**2 - 14*x/(x**2 + 10) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (-7*x**2 - 3)/(x**2 + 10)", "id": "calculus-L2-65eebb136cd4652b590c", "source_id": "calculus-65eebb136cd4652b590c", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(-7*x**2 - 3)/(x**2 + 10)**2 - 14*x/(x**2 + 10) with respect to x.", "answer": "(-7*x**2 - 3)/(x**2 + 10)", "expr": "-2*x*(-7*x**2 - 3)/(x**2 + 10)**2 - 14*x/(x**2 + 10)", "primitive": "(-7*x**2 - 3)/(x**2 + 10)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 5*(-4*x**3 + 9*x**2 + 14*x - 4)*cos(9*x + 23) - 45*(-x**4 + 3*x**3 + 7*x**2 - 4*x - 7)*sin(9*x + 23) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 5*(-x**4 + 3*x**3 + 7*x**2 - 4*x - 7)*cos(9*x + 23)", "id": "calculus-L2-72712f7b7ea2f23ceb22", "source_id": "calculus-72712f7b7ea2f23ceb22", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 5*(-4*x**3 + 9*x**2 + 14*x - 4)*cos(9*x + 23) - 45*(-x**4 + 3*x**3 + 7*x**2 - 4*x - 7)*sin(9*x + 23) with respect to x.", "answer": "5*(-x**4 + 3*x**3 + 7*x**2 - 4*x - 7)*cos(9*x + 23)", "expr": "5*(-4*x**3 + 9*x**2 + 14*x - 4)*cos(9*x + 23) - 45*(-x**4 + 3*x**3 + 7*x**2 - 4*x - 7)*sin(9*x + 23)", "primitive": "5*(-x**4 + 3*x**3 + 7*x**2 - 4*x - 7)*cos(9*x + 23)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 6*x*exp(x**2 + 5) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 3*exp(x**2 + 5)", "id": "calculus-L2-29e36cee300abdf0042c", "source_id": "calculus-29e36cee300abdf0042c", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 6*x*exp(x**2 + 5) with respect to x.", "answer": "3*exp(x**2 + 5)", "expr": "6*x*exp(x**2 + 5)", "primitive": "3*exp(x**2 + 5)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = sin(3*x)*cos(20*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -20*sin(3*x)*sin(20*x) + 3*cos(3*x)*cos(20*x)", "id": "calculus-L2-dbf8310c78454c9cf1c6", "source_id": "calculus-dbf8310c78454c9cf1c6", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = sin(3*x)*cos(20*x) with respect to x.", "answer": "-20*sin(3*x)*sin(20*x) + 3*cos(3*x)*cos(20*x)", "expr": "sin(3*x)*cos(20*x)", "primitive": "sin(3*x)*cos(20*x)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(9*x**3 - 8*x**2 + 6*x - 8)/(x**2 + 14)**2 + (27*x**2 - 16*x + 6)/(x**2 + 14) with respect to x from 0 to 1. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 53/105", "id": "calculus-L2-d079d243aa0dc5fd4f10", "source_id": "calculus-d079d243aa0dc5fd4f10", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(9*x**3 - 8*x**2 + 6*x - 8)/(x**2 + 14)**2 + (27*x**2 - 16*x + 6)/(x**2 + 14) with respect to x from 0 to 1.", "answer": "53/105", "expr": "-2*x*(9*x**3 - 8*x**2 + 6*x - 8)/(x**2 + 14)**2 + (27*x**2 - 16*x + 6)/(x**2 + 14)", "primitive": "(9*x**3 - 8*x**2 + 6*x - 8)/(x**2 + 14)", "lower": "0", "upper": "1", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (7 - 9*x)/(x**2 + 12) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(7 - 9*x)/(x**2 + 12)**2 - 9/(x**2 + 12)", "id": "calculus-L2-1944ce032cd17eb05091", "source_id": "calculus-1944ce032cd17eb05091", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (7 - 9*x)/(x**2 + 12) with respect to x.", "answer": "-2*x*(7 - 9*x)/(x**2 + 12)**2 - 9/(x**2 + 12)", "expr": "(7 - 9*x)/(x**2 + 12)", "primitive": "(7 - 9*x)/(x**2 + 12)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (-4*x**2 - 7*x - 5)/(x**2 + 19) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(-4*x**2 - 7*x - 5)/(x**2 + 19)**2 + (-8*x - 7)/(x**2 + 19)", "id": "calculus-L2-943e705f6613e2273d43", "source_id": "calculus-943e705f6613e2273d43", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (-4*x**2 - 7*x - 5)/(x**2 + 19) with respect to x.", "answer": "-2*x*(-4*x**2 - 7*x - 5)/(x**2 + 19)**2 + (-8*x - 7)/(x**2 + 19)", "expr": "(-4*x**2 - 7*x - 5)/(x**2 + 19)", "primitive": "(-4*x**2 - 7*x - 5)/(x**2 + 19)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(-7*x**3 + 4*x**2 - 2*x + 6)/(x**2 + 6)**2 + (-21*x**2 + 8*x - 2)/(x**2 + 6) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (-7*x**3 + 4*x**2 - 2*x + 6)/(x**2 + 6)", "id": "calculus-L2-3e1f9eb426c02bdd373e", "source_id": "calculus-3e1f9eb426c02bdd373e", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(-7*x**3 + 4*x**2 - 2*x + 6)/(x**2 + 6)**2 + (-21*x**2 + 8*x - 2)/(x**2 + 6) with respect to x.", "answer": "(-7*x**3 + 4*x**2 - 2*x + 6)/(x**2 + 6)", "expr": "-2*x*(-7*x**3 + 4*x**2 - 2*x + 6)/(x**2 + 6)**2 + (-21*x**2 + 8*x - 2)/(x**2 + 6)", "primitive": "(-7*x**3 + 4*x**2 - 2*x + 6)/(x**2 + 6)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (-x**2 - 6*x)/(x**2 + 12) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(-x**2 - 6*x)/(x**2 + 12)**2 + (-2*x - 6)/(x**2 + 12)", "id": "calculus-L2-d4ac2a54b2d4f126bd91", "source_id": "calculus-d4ac2a54b2d4f126bd91", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (-x**2 - 6*x)/(x**2 + 12) with respect to x.", "answer": "-2*x*(-x**2 - 6*x)/(x**2 + 12)**2 + (-2*x - 6)/(x**2 + 12)", "expr": "(-x**2 - 6*x)/(x**2 + 12)", "primitive": "(-x**2 - 6*x)/(x**2 + 12)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 14*(8*x**3 + 5*x**2 - 8*x + 5)*sin(2*x + 19) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 14*(24*x**2 + 10*x - 8)*sin(2*x + 19) + 28*(8*x**3 + 5*x**2 - 8*x + 5)*cos(2*x + 19)", "id": "calculus-L2-e85799a3d2768db5b764", "source_id": "calculus-e85799a3d2768db5b764", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 14*(8*x**3 + 5*x**2 - 8*x + 5)*sin(2*x + 19) with respect to x.", "answer": "14*(24*x**2 + 10*x - 8)*sin(2*x + 19) + 28*(8*x**3 + 5*x**2 - 8*x + 5)*cos(2*x + 19)", "expr": "14*(8*x**3 + 5*x**2 - 8*x + 5)*sin(2*x + 19)", "primitive": "14*(8*x**3 + 5*x**2 - 8*x + 5)*sin(2*x + 19)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 300*sin(3*x + 28)*cos(8*x + 15) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2400*sin(3*x + 28)*sin(8*x + 15) + 900*cos(3*x + 28)*cos(8*x + 15)", "id": "calculus-L2-9359c6b961dadbaccd95", "source_id": "calculus-9359c6b961dadbaccd95", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 300*sin(3*x + 28)*cos(8*x + 15) with respect to x.", "answer": "-2400*sin(3*x + 28)*sin(8*x + 15) + 900*cos(3*x + 28)*cos(8*x + 15)", "expr": "300*sin(3*x + 28)*cos(8*x + 15)", "primitive": "300*sin(3*x + 28)*cos(8*x + 15)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 6*exp(8*x**2 + 20) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 96*x*exp(8*x**2 + 20)", "id": "calculus-L2-6b5b69a7fb071b1a51e5", "source_id": "calculus-6b5b69a7fb071b1a51e5", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 6*exp(8*x**2 + 20) with respect to x.", "answer": "96*x*exp(8*x**2 + 20)", "expr": "6*exp(8*x**2 + 20)", "primitive": "6*exp(8*x**2 + 20)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (6*exp(3*x) + 18)*log(x + 13) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 18*exp(3*x)*log(x + 13) + (6*exp(3*x) + 18)/(x + 13)", "id": "calculus-L2-2eaafbfc60578c304292", "source_id": "calculus-2eaafbfc60578c304292", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (6*exp(3*x) + 18)*log(x + 13) with respect to x.", "answer": "18*exp(3*x)*log(x + 13) + (6*exp(3*x) + 18)/(x + 13)", "expr": "(6*exp(3*x) + 18)*log(x + 13)", "primitive": "(6*exp(3*x) + 18)*log(x + 13)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 2079*sin(5*x + 10)*cos(9*x + 10) + 1155*sin(9*x + 10)*cos(5*x + 10) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 231*sin(5*x + 10)*sin(9*x + 10)", "id": "calculus-L2-2c6fb684fa05e7f73c53", "source_id": "calculus-2c6fb684fa05e7f73c53", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 2079*sin(5*x + 10)*cos(9*x + 10) + 1155*sin(9*x + 10)*cos(5*x + 10) with respect to x.", "answer": "231*sin(5*x + 10)*sin(9*x + 10)", "expr": "2079*sin(5*x + 10)*cos(9*x + 10) + 1155*sin(9*x + 10)*cos(5*x + 10)", "primitive": "231*sin(5*x + 10)*sin(9*x + 10)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(2*x + 9)/(x**2 + 11)**2 + 2/(x**2 + 11) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (2*x + 9)/(x**2 + 11)", "id": "calculus-L2-b656edea6225f6f3ad20", "source_id": "calculus-b656edea6225f6f3ad20", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(2*x + 9)/(x**2 + 11)**2 + 2/(x**2 + 11) with respect to x.", "answer": "(2*x + 9)/(x**2 + 11)", "expr": "-2*x*(2*x + 9)/(x**2 + 11)**2 + 2/(x**2 + 11)", "primitive": "(2*x + 9)/(x**2 + 11)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 4*(-3*x**4 - 7*x**3 - 4*x**2 + 5)*log(11*x + 6) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 4*(-12*x**3 - 21*x**2 - 8*x)*log(11*x + 6) + 44*(-3*x**4 - 7*x**3 - 4*x**2 + 5)/(11*x + 6)", "id": "calculus-L2-648951a784159281f448", "source_id": "calculus-648951a784159281f448", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 4*(-3*x**4 - 7*x**3 - 4*x**2 + 5)*log(11*x + 6) with respect to x.", "answer": "4*(-12*x**3 - 21*x**2 - 8*x)*log(11*x + 6) + 44*(-3*x**4 - 7*x**3 - 4*x**2 + 5)/(11*x + 6)", "expr": "4*(-3*x**4 - 7*x**3 - 4*x**2 + 5)*log(11*x + 6)", "primitive": "4*(-3*x**4 - 7*x**3 - 4*x**2 + 5)*log(11*x + 6)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 8*x*exp(4*x**2 + 6) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: exp(4*x**2 + 6)", "id": "calculus-L2-162b877e0eead6e42eda", "source_id": "calculus-162b877e0eead6e42eda", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 8*x*exp(4*x**2 + 6) with respect to x.", "answer": "exp(4*x**2 + 6)", "expr": "8*x*exp(4*x**2 + 6)", "primitive": "exp(4*x**2 + 6)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(-2*x**2 - 2*x + 8)/(x**2 + 13)**2 + (-4*x - 2)/(x**2 + 13) with respect to x from 1 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -78/77", "id": "calculus-L2-6a2b097dd7dbb508eee6", "source_id": "calculus-6a2b097dd7dbb508eee6", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(-2*x**2 - 2*x + 8)/(x**2 + 13)**2 + (-4*x - 2)/(x**2 + 13) with respect to x from 1 to 3.", "answer": "-78/77", "expr": "-2*x*(-2*x**2 - 2*x + 8)/(x**2 + 13)**2 + (-4*x - 2)/(x**2 + 13)", "primitive": "(-2*x**2 - 2*x + 8)/(x**2 + 13)", "lower": "1", "upper": "3", "split": "dev"}
{"instruction": "Evaluate the definite integral of -990*log(12*x + 2)*sin(9*x + 8) + 1320*cos(9*x + 8)/(12*x + 2) with respect to x from 1 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 110*log(38)*cos(35) - 110*log(14)*cos(17)", "id": "calculus-L2-08c0ee9254a9dcba87e8", "source_id": "calculus-08c0ee9254a9dcba87e8", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -990*log(12*x + 2)*sin(9*x + 8) + 1320*cos(9*x + 8)/(12*x + 2) with respect to x from 1 to 3.", "answer": "110*log(38)*cos(35) - 110*log(14)*cos(17)", "expr": "-990*log(12*x + 2)*sin(9*x + 8) + 1320*cos(9*x + 8)/(12*x + 2)", "primitive": "110*log(12*x + 2)*cos(9*x + 8)", "lower": "1", "upper": "3", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 7*exp(5*x**2 + 20) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 70*x*exp(5*x**2 + 20)", "id": "calculus-L2-ecd565a0ddfa6e652271", "source_id": "calculus-ecd565a0ddfa6e652271", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 7*exp(5*x**2 + 20) with respect to x.", "answer": "70*x*exp(5*x**2 + 20)", "expr": "7*exp(5*x**2 + 20)", "primitive": "7*exp(5*x**2 + 20)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(-x**2 - 7*x + 2)/(x**2 + 6)**2 + (-2*x - 7)/(x**2 + 6) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (-x**2 - 7*x + 2)/(x**2 + 6)", "id": "calculus-L2-66fac2c5bc443c4966b0", "source_id": "calculus-66fac2c5bc443c4966b0", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(-x**2 - 7*x + 2)/(x**2 + 6)**2 + (-2*x - 7)/(x**2 + 6) with respect to x.", "answer": "(-x**2 - 7*x + 2)/(x**2 + 6)", "expr": "-2*x*(-x**2 - 7*x + 2)/(x**2 + 6)**2 + (-2*x - 7)/(x**2 + 6)", "primitive": "(-x**2 - 7*x + 2)/(x**2 + 6)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 42*x*exp(7*x**2 + 14) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 3*exp(7*x**2 + 14)", "id": "calculus-L2-e6eff1b0b6a4470c6977", "source_id": "calculus-e6eff1b0b6a4470c6977", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 42*x*exp(7*x**2 + 14) with respect to x.", "answer": "3*exp(7*x**2 + 14)", "expr": "42*x*exp(7*x**2 + 14)", "primitive": "3*exp(7*x**2 + 14)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 14*(26*exp(10*x) + 3)*cos(7*x + 10) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -98*(26*exp(10*x) + 3)*sin(7*x + 10) + 3640*exp(10*x)*cos(7*x + 10)", "id": "calculus-L2-378e2c774283a12ee601", "source_id": "calculus-378e2c774283a12ee601", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 14*(26*exp(10*x) + 3)*cos(7*x + 10) with respect to x.", "answer": "-98*(26*exp(10*x) + 3)*sin(7*x + 10) + 3640*exp(10*x)*cos(7*x + 10)", "expr": "14*(26*exp(10*x) + 3)*cos(7*x + 10)", "primitive": "14*(26*exp(10*x) + 3)*cos(7*x + 10)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (25*exp(8*x) + 25)*(5*x**2 + 4*x - 6) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (10*x + 4)*(25*exp(8*x) + 25) + 200*(5*x**2 + 4*x - 6)*exp(8*x)", "id": "calculus-L2-14b0b9c1c93833132824", "source_id": "calculus-14b0b9c1c93833132824", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (25*exp(8*x) + 25)*(5*x**2 + 4*x - 6) with respect to x.", "answer": "(10*x + 4)*(25*exp(8*x) + 25) + 200*(5*x**2 + 4*x - 6)*exp(8*x)", "expr": "(25*exp(8*x) + 25)*(5*x**2 + 4*x - 6)", "primitive": "(25*exp(8*x) + 25)*(5*x**2 + 4*x - 6)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -1311*log(x + 14)*sin(3*x + 17) + 437*cos(3*x + 17)/(x + 14) with respect to x from 0 to 1. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -437*log(14)*cos(17) + 437*log(15)*cos(20)", "id": "calculus-L2-fd017ad2c3744cc1c193", "source_id": "calculus-fd017ad2c3744cc1c193", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -1311*log(x + 14)*sin(3*x + 17) + 437*cos(3*x + 17)/(x + 14) with respect to x from 0 to 1.", "answer": "-437*log(14)*cos(17) + 437*log(15)*cos(20)", "expr": "-1311*log(x + 14)*sin(3*x + 17) + 437*cos(3*x + 17)/(x + 14)", "primitive": "437*log(x + 14)*cos(3*x + 17)", "lower": "0", "upper": "1", "split": "dev"}
{"instruction": "Evaluate the definite integral of -20*sin(5*x)*sin(20*x) + 5*cos(5*x)*cos(20*x) with respect to x from 0 to 2. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: sin(10)*cos(40)", "id": "calculus-L2-9bb2014925ac5f3a39bd", "source_id": "calculus-9bb2014925ac5f3a39bd", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -20*sin(5*x)*sin(20*x) + 5*cos(5*x)*cos(20*x) with respect to x from 0 to 2.", "answer": "sin(10)*cos(40)", "expr": "-20*sin(5*x)*sin(20*x) + 5*cos(5*x)*cos(20*x)", "primitive": "sin(5*x)*cos(20*x)", "lower": "0", "upper": "2", "split": "dev"}
{"instruction": "Find the derivative of f(x) = sin(2*x)*cos(5*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -5*sin(2*x)*sin(5*x) + 2*cos(2*x)*cos(5*x)", "id": "calculus-L2-e97eb5592d0a081e8e06", "source_id": "calculus-e97eb5592d0a081e8e06", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = sin(2*x)*cos(5*x) with respect to x.", "answer": "-5*sin(2*x)*sin(5*x) + 2*cos(2*x)*cos(5*x)", "expr": "sin(2*x)*cos(5*x)", "primitive": "sin(2*x)*cos(5*x)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -10*sin(9*x)*sin(10*x) + 9*cos(9*x)*cos(10*x) with respect to x from 2 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: sin(27)*cos(30) - sin(18)*cos(20)", "id": "calculus-L2-e7307894b6b2594fe05d", "source_id": "calculus-e7307894b6b2594fe05d", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -10*sin(9*x)*sin(10*x) + 9*cos(9*x)*cos(10*x) with respect to x from 2 to 3.", "answer": "sin(27)*cos(30) - sin(18)*cos(20)", "expr": "-10*sin(9*x)*sin(10*x) + 9*cos(9*x)*cos(10*x)", "primitive": "sin(9*x)*cos(10*x)", "lower": "2", "upper": "3", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 5*(3*x**2 - 2*x - 2)*cos(9*x + 8) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 5*(6*x - 2)*cos(9*x + 8) - 45*(3*x**2 - 2*x - 2)*sin(9*x + 8)", "id": "calculus-L2-a22b9bae8f1e74f407ce", "source_id": "calculus-a22b9bae8f1e74f407ce", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 5*(3*x**2 - 2*x - 2)*cos(9*x + 8) with respect to x.", "answer": "5*(6*x - 2)*cos(9*x + 8) - 45*(3*x**2 - 2*x - 2)*sin(9*x + 8)", "expr": "5*(3*x**2 - 2*x - 2)*cos(9*x + 8)", "primitive": "5*(3*x**2 - 2*x - 2)*cos(9*x + 8)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 16*exp(x**2 + 15) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 32*x*exp(x**2 + 15)", "id": "calculus-L2-418d6ade14373ca50cc1", "source_id": "calculus-418d6ade14373ca50cc1", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 16*exp(x**2 + 15) with respect to x.", "answer": "32*x*exp(x**2 + 15)", "expr": "16*exp(x**2 + 15)", "primitive": "16*exp(x**2 + 15)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 17*exp(8*x**2 + 19) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 272*x*exp(8*x**2 + 19)", "id": "calculus-L2-2ca3087940d8411f9b47", "source_id": "calculus-2ca3087940d8411f9b47", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 17*exp(8*x**2 + 19) with respect to x.", "answer": "272*x*exp(8*x**2 + 19)", "expr": "17*exp(8*x**2 + 19)", "primitive": "17*exp(8*x**2 + 19)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 126*log(8*x + 6)*cos(7*x + 9) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -882*log(8*x + 6)*sin(7*x + 9) + 1008*cos(7*x + 9)/(8*x + 6)", "id": "calculus-L2-84d02a09015fd2cd6902", "source_id": "calculus-84d02a09015fd2cd6902", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 126*log(8*x + 6)*cos(7*x + 9) with respect to x.", "answer": "-882*log(8*x + 6)*sin(7*x + 9) + 1008*cos(7*x + 9)/(8*x + 6)", "expr": "126*log(8*x + 6)*cos(7*x + 9)", "primitive": "126*log(8*x + 6)*cos(7*x + 9)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (-5*x**2 + 4*x - 4)/(x**2 + 12) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(-5*x**2 + 4*x - 4)/(x**2 + 12)**2 + (4 - 10*x)/(x**2 + 12)", "id": "calculus-L2-2623cc7cc88c081da28a", "source_id": "calculus-2623cc7cc88c081da28a", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (-5*x**2 + 4*x - 4)/(x**2 + 12) with respect to x.", "answer": "-2*x*(-5*x**2 + 4*x - 4)/(x**2 + 12)**2 + (4 - 10*x)/(x**2 + 12)", "expr": "(-5*x**2 + 4*x - 4)/(x**2 + 12)", "primitive": "(-5*x**2 + 4*x - 4)/(x**2 + 12)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(4*x**2 + 5*x - 8)/(x**2 + 5)**2 + (8*x + 5)/(x**2 + 5) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (4*x**2 + 5*x - 8)/(x**2 + 5)", "id": "calculus-L2-a3e219ed476c5cf3cece", "source_id": "calculus-a3e219ed476c5cf3cece", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(4*x**2 + 5*x - 8)/(x**2 + 5)**2 + (8*x + 5)/(x**2 + 5) with respect to x.", "answer": "(4*x**2 + 5*x - 8)/(x**2 + 5)", "expr": "-2*x*(4*x**2 + 5*x - 8)/(x**2 + 5)**2 + (8*x + 5)/(x**2 + 5)", "primitive": "(4*x**2 + 5*x - 8)/(x**2 + 5)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 320*x*exp(8*x**2 + 20) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 20*exp(8*x**2 + 20)", "id": "calculus-L2-b00b6a117d5e814880a7", "source_id": "calculus-b00b6a117d5e814880a7", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 320*x*exp(8*x**2 + 20) with respect to x.", "answer": "20*exp(8*x**2 + 20)", "expr": "320*x*exp(8*x**2 + 20)", "primitive": "20*exp(8*x**2 + 20)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (9*x**2 - 7*x - 8)/(x**2 + 14) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(9*x**2 - 7*x - 8)/(x**2 + 14)**2 + (18*x - 7)/(x**2 + 14)", "id": "calculus-L2-53cd9dffd69ee8e4f320", "source_id": "calculus-53cd9dffd69ee8e4f320", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (9*x**2 - 7*x - 8)/(x**2 + 14) with respect to x.", "answer": "-2*x*(9*x**2 - 7*x - 8)/(x**2 + 14)**2 + (18*x - 7)/(x**2 + 14)", "expr": "(9*x**2 - 7*x - 8)/(x**2 + 14)", "primitive": "(9*x**2 - 7*x - 8)/(x**2 + 14)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = sin(3*x)*cos(16*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -16*sin(3*x)*sin(16*x) + 3*cos(3*x)*cos(16*x)", "id": "calculus-L2-dae3f63fcb99819489bc", "source_id": "calculus-dae3f63fcb99819489bc", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = sin(3*x)*cos(16*x) with respect to x.", "answer": "-16*sin(3*x)*sin(16*x) + 3*cos(3*x)*cos(16*x)", "expr": "sin(3*x)*cos(16*x)", "primitive": "sin(3*x)*cos(16*x)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 50*x*exp(5*x**2 + 6) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 5*exp(5*x**2 + 6)", "id": "calculus-L2-66066b611751b34e547d", "source_id": "calculus-66066b611751b34e547d", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 50*x*exp(5*x**2 + 6) with respect to x.", "answer": "5*exp(5*x**2 + 6)", "expr": "50*x*exp(5*x**2 + 6)", "primitive": "5*exp(5*x**2 + 6)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 870*cos(5*x + 21)*cos(11*x + 19) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -4350*sin(5*x + 21)*cos(11*x + 19) - 9570*sin(11*x + 19)*cos(5*x + 21)", "id": "calculus-L2-4bd885d77e0c48bbd4e0", "source_id": "calculus-4bd885d77e0c48bbd4e0", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 870*cos(5*x + 21)*cos(11*x + 19) with respect to x.", "answer": "-4350*sin(5*x + 21)*cos(11*x + 19) - 9570*sin(11*x + 19)*cos(5*x + 21)", "expr": "870*cos(5*x + 21)*cos(11*x + 19)", "primitive": "870*cos(5*x + 21)*cos(11*x + 19)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 29*(27*exp(10*x) + 10)*sin(9*x + 20) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 261*(27*exp(10*x) + 10)*cos(9*x + 20) + 7830*exp(10*x)*sin(9*x + 20)", "id": "calculus-L2-264259489f2c23b38947", "source_id": "calculus-264259489f2c23b38947", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 29*(27*exp(10*x) + 10)*sin(9*x + 20) with respect to x.", "answer": "261*(27*exp(10*x) + 10)*cos(9*x + 20) + 7830*exp(10*x)*sin(9*x + 20)", "expr": "29*(27*exp(10*x) + 10)*sin(9*x + 20)", "primitive": "29*(27*exp(10*x) + 10)*sin(9*x + 20)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = sin(3*x)*cos(9*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -9*sin(3*x)*sin(9*x) + 3*cos(3*x)*cos(9*x)", "id": "calculus-L2-410bb24defa8785e68da", "source_id": "calculus-410bb24defa8785e68da", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = sin(3*x)*cos(9*x) with respect to x.", "answer": "-9*sin(3*x)*sin(9*x) + 3*cos(3*x)*cos(9*x)", "expr": "sin(3*x)*cos(9*x)", "primitive": "sin(3*x)*cos(9*x)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 200*x*exp(5*x**2 + 12) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 20*exp(5*x**2 + 12)", "id": "calculus-L2-b604e05f853830f1bbc3", "source_id": "calculus-b604e05f853830f1bbc3", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 200*x*exp(5*x**2 + 12) with respect to x.", "answer": "20*exp(5*x**2 + 12)", "expr": "200*x*exp(5*x**2 + 12)", "primitive": "20*exp(5*x**2 + 12)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(4*x**3 + 4*x**2 - x - 9)/(x**2 + 4)**2 + (12*x**2 + 8*x - 1)/(x**2 + 4) with respect to x from 0 to 2. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 55/8", "id": "calculus-L2-c9c9f73cb11bc0822958", "source_id": "calculus-c9c9f73cb11bc0822958", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(4*x**3 + 4*x**2 - x - 9)/(x**2 + 4)**2 + (12*x**2 + 8*x - 1)/(x**2 + 4) with respect to x from 0 to 2.", "answer": "55/8", "expr": "-2*x*(4*x**3 + 4*x**2 - x - 9)/(x**2 + 4)**2 + (12*x**2 + 8*x - 1)/(x**2 + 4)", "primitive": "(4*x**3 + 4*x**2 - x - 9)/(x**2 + 4)", "lower": "0", "upper": "2", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(-6*x**2 + 8*x + 5)/(x**2 + 3)**2 + (8 - 12*x)/(x**2 + 3) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (-6*x**2 + 8*x + 5)/(x**2 + 3)", "id": "calculus-L2-840d0b1d6fc1eb67d03d", "source_id": "calculus-840d0b1d6fc1eb67d03d", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(-6*x**2 + 8*x + 5)/(x**2 + 3)**2 + (8 - 12*x)/(x**2 + 3) with respect to x.", "answer": "(-6*x**2 + 8*x + 5)/(x**2 + 3)", "expr": "-2*x*(-6*x**2 + 8*x + 5)/(x**2 + 3)**2 + (8 - 12*x)/(x**2 + 3)", "primitive": "(-6*x**2 + 8*x + 5)/(x**2 + 3)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -448*sin(7*x + 1)*cos(9*x + 2) - 576*sin(9*x + 2)*cos(7*x + 1) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 64*cos(7*x + 1)*cos(9*x + 2)", "id": "calculus-L2-d909d7fae08d8c224384", "source_id": "calculus-d909d7fae08d8c224384", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -448*sin(7*x + 1)*cos(9*x + 2) - 576*sin(9*x + 2)*cos(7*x + 1) with respect to x.", "answer": "64*cos(7*x + 1)*cos(9*x + 2)", "expr": "-448*sin(7*x + 1)*cos(9*x + 2) - 576*sin(9*x + 2)*cos(7*x + 1)", "primitive": "64*cos(7*x + 1)*cos(9*x + 2)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 702*sin(9*x + 21)*cos(10*x + 7) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -7020*sin(9*x + 21)*sin(10*x + 7) + 6318*cos(9*x + 21)*cos(10*x + 7)", "id": "calculus-L2-d86443151734aa8f1bf5", "source_id": "calculus-d86443151734aa8f1bf5", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 702*sin(9*x + 21)*cos(10*x + 7) with respect to x.", "answer": "-7020*sin(9*x + 21)*sin(10*x + 7) + 6318*cos(9*x + 21)*cos(10*x + 7)", "expr": "702*sin(9*x + 21)*cos(10*x + 7)", "primitive": "702*sin(9*x + 21)*cos(10*x + 7)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of 27*(-15*x**2 + 10*x + 6)*sin(8*x + 19) + 216*(-5*x**3 + 5*x**2 + 6*x + 3)*cos(8*x + 19) with respect to x from 0 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -81*sin(19) - 1863*sin(43)", "id": "calculus-L2-12296cc033199059550f", "source_id": "calculus-12296cc033199059550f", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of 27*(-15*x**2 + 10*x + 6)*sin(8*x + 19) + 216*(-5*x**3 + 5*x**2 + 6*x + 3)*cos(8*x + 19) with respect to x from 0 to 3.", "answer": "-81*sin(19) - 1863*sin(43)", "expr": "27*(-15*x**2 + 10*x + 6)*sin(8*x + 19) + 216*(-5*x**3 + 5*x**2 + 6*x + 3)*cos(8*x + 19)", "primitive": "27*(-5*x**3 + 5*x**2 + 6*x + 3)*sin(8*x + 19)", "lower": "0", "upper": "3", "split": "dev"}
{"instruction": "Evaluate the definite integral of -594*log(11*x + 30)*sin(3*x + 6) + 2178*cos(3*x + 6)/(11*x + 30) with respect to x from 2 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -198*log(52)*cos(12) + 198*log(63)*cos(15)", "id": "calculus-L2-22e36e63847555b45398", "source_id": "calculus-22e36e63847555b45398", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -594*log(11*x + 30)*sin(3*x + 6) + 2178*cos(3*x + 6)/(11*x + 30) with respect to x from 2 to 3.", "answer": "-198*log(52)*cos(12) + 198*log(63)*cos(15)", "expr": "-594*log(11*x + 30)*sin(3*x + 6) + 2178*cos(3*x + 6)/(11*x + 30)", "primitive": "198*log(11*x + 30)*cos(3*x + 6)", "lower": "2", "upper": "3", "split": "dev"}
{"instruction": "Find the derivative of f(x) = sin(7*x)*cos(9*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -9*sin(7*x)*sin(9*x) + 7*cos(7*x)*cos(9*x)", "id": "calculus-L2-4fe7ce1fe81b1eb5716a", "source_id": "calculus-4fe7ce1fe81b1eb5716a", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = sin(7*x)*cos(9*x) with respect to x.", "answer": "-9*sin(7*x)*sin(9*x) + 7*cos(7*x)*cos(9*x)", "expr": "sin(7*x)*cos(9*x)", "primitive": "sin(7*x)*cos(9*x)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 38*x*exp(x**2 + 9) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 19*exp(x**2 + 9)", "id": "calculus-L2-f9caa1f2ae8762f0403e", "source_id": "calculus-f9caa1f2ae8762f0403e", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 38*x*exp(x**2 + 9) with respect to x.", "answer": "19*exp(x**2 + 9)", "expr": "38*x*exp(x**2 + 9)", "primitive": "19*exp(x**2 + 9)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -12*sin(7*x)*sin(12*x) + 7*cos(7*x)*cos(12*x) with respect to x from 1 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -sin(7)*cos(12) + sin(21)*cos(36)", "id": "calculus-L2-a74083ec6e0abf098861", "source_id": "calculus-a74083ec6e0abf098861", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -12*sin(7*x)*sin(12*x) + 7*cos(7*x)*cos(12*x) with respect to x from 1 to 3.", "answer": "-sin(7)*cos(12) + sin(21)*cos(36)", "expr": "-12*sin(7*x)*sin(12*x) + 7*cos(7*x)*cos(12*x)", "primitive": "sin(7*x)*cos(12*x)", "lower": "1", "upper": "3", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 14*exp(8*x**2 + 9) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 224*x*exp(8*x**2 + 9)", "id": "calculus-L2-b80dac32611f0523af9e", "source_id": "calculus-b80dac32611f0523af9e", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 14*exp(8*x**2 + 9) with respect to x.", "answer": "224*x*exp(8*x**2 + 9)", "expr": "14*exp(8*x**2 + 9)", "primitive": "14*exp(8*x**2 + 9)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (9*x**3 + x - 8)/(x**2 + 8) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(9*x**3 + x - 8)/(x**2 + 8)**2 + (27*x**2 + 1)/(x**2 + 8)", "id": "calculus-L2-129983748cb0a7404f8c", "source_id": "calculus-129983748cb0a7404f8c", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (9*x**3 + x - 8)/(x**2 + 8) with respect to x.", "answer": "-2*x*(9*x**3 + x - 8)/(x**2 + 8)**2 + (27*x**2 + 1)/(x**2 + 8)", "expr": "(9*x**3 + x - 8)/(x**2 + 8)", "primitive": "(9*x**3 + x - 8)/(x**2 + 8)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (-2*x**3 + x - 3)/(x**2 + 2) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(-2*x**3 + x - 3)/(x**2 + 2)**2 + (1 - 6*x**2)/(x**2 + 2)", "id": "calculus-L2-a79f1365e606f47899a9", "source_id": "calculus-a79f1365e606f47899a9", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (-2*x**3 + x - 3)/(x**2 + 2) with respect to x.", "answer": "-2*x*(-2*x**3 + x - 3)/(x**2 + 2)**2 + (1 - 6*x**2)/(x**2 + 2)", "expr": "(-2*x**3 + x - 3)/(x**2 + 2)", "primitive": "(-2*x**3 + x - 3)/(x**2 + 2)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (4*x**3 - 6*x**2 - 8)/(x**2 + 8) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(4*x**3 - 6*x**2 - 8)/(x**2 + 8)**2 + (12*x**2 - 12*x)/(x**2 + 8)", "id": "calculus-L2-7e301e71a133fec1caef", "source_id": "calculus-7e301e71a133fec1caef", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (4*x**3 - 6*x**2 - 8)/(x**2 + 8) with respect to x.", "answer": "-2*x*(4*x**3 - 6*x**2 - 8)/(x**2 + 8)**2 + (12*x**2 - 12*x)/(x**2 + 8)", "expr": "(4*x**3 - 6*x**2 - 8)/(x**2 + 8)", "primitive": "(4*x**3 - 6*x**2 - 8)/(x**2 + 8)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (-2*x**3 - 2*x**2 - 6)*(-5*x**3 + 3*x**2 - 8*x + 9) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (-6*x**2 - 4*x)*(-5*x**3 + 3*x**2 - 8*x + 9) + (-15*x**2 + 6*x - 8)*(-2*x**3 - 2*x**2 - 6)", "id": "calculus-L2-f941848417d3383a1458", "source_id": "calculus-f941848417d3383a1458", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (-2*x**3 - 2*x**2 - 6)*(-5*x**3 + 3*x**2 - 8*x + 9) with respect to x.", "answer": "(-6*x**2 - 4*x)*(-5*x**3 + 3*x**2 - 8*x + 9) + (-15*x**2 + 6*x - 8)*(-2*x**3 - 2*x**2 - 6)", "expr": "(-2*x**3 - 2*x**2 - 6)*(-5*x**3 + 3*x**2 - 8*x + 9)", "primitive": "(-2*x**3 - 2*x**2 - 6)*(-5*x**3 + 3*x**2 - 8*x + 9)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 14*exp(x**2 + 13) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 28*x*exp(x**2 + 13)", "id": "calculus-L2-98ee3d13ed8cf816fbdb", "source_id": "calculus-98ee3d13ed8cf816fbdb", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 14*exp(x**2 + 13) with respect to x.", "answer": "28*x*exp(x**2 + 13)", "expr": "14*exp(x**2 + 13)", "primitive": "14*exp(x**2 + 13)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (9 - 6*x)/(x**2 + 7) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(9 - 6*x)/(x**2 + 7)**2 - 6/(x**2 + 7)", "id": "calculus-L2-66c65831e0bdfdb1ebbf", "source_id": "calculus-66c65831e0bdfdb1ebbf", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (9 - 6*x)/(x**2 + 7) with respect to x.", "answer": "-2*x*(9 - 6*x)/(x**2 + 7)**2 - 6/(x**2 + 7)", "expr": "(9 - 6*x)/(x**2 + 7)", "primitive": "(9 - 6*x)/(x**2 + 7)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 432*log(5*x + 3)*cos(5*x + 9) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2160*log(5*x + 3)*sin(5*x + 9) + 2160*cos(5*x + 9)/(5*x + 3)", "id": "calculus-L2-381a54aa164753006355", "source_id": "calculus-381a54aa164753006355", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 432*log(5*x + 3)*cos(5*x + 9) with respect to x.", "answer": "-2160*log(5*x + 3)*sin(5*x + 9) + 2160*cos(5*x + 9)/(5*x + 3)", "expr": "432*log(5*x + 3)*cos(5*x + 9)", "primitive": "432*log(5*x + 3)*cos(5*x + 9)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 77*log(9*x + 15)*sin(12*x + 24) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 924*log(9*x + 15)*cos(12*x + 24) + 693*sin(12*x + 24)/(9*x + 15)", "id": "calculus-L2-3896fb54bcd85e98a600", "source_id": "calculus-3896fb54bcd85e98a600", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 77*log(9*x + 15)*sin(12*x + 24) with respect to x.", "answer": "924*log(9*x + 15)*cos(12*x + 24) + 693*sin(12*x + 24)/(9*x + 15)", "expr": "77*log(9*x + 15)*sin(12*x + 24)", "primitive": "77*log(9*x + 15)*sin(12*x + 24)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 1088*exp(4*x)*log(3*x + 23) + 48*(17*exp(4*x) + 23)/(3*x + 23) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 16*(17*exp(4*x) + 23)*log(3*x + 23)", "id": "calculus-L2-5f573622981145b90d14", "source_id": "calculus-5f573622981145b90d14", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 1088*exp(4*x)*log(3*x + 23) + 48*(17*exp(4*x) + 23)/(3*x + 23) with respect to x.", "answer": "16*(17*exp(4*x) + 23)*log(3*x + 23)", "expr": "1088*exp(4*x)*log(3*x + 23) + 48*(17*exp(4*x) + 23)/(3*x + 23)", "primitive": "16*(17*exp(4*x) + 23)*log(3*x + 23)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 32*x*exp(2*x**2 + 15) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 8*exp(2*x**2 + 15)", "id": "calculus-L2-df98332989bf699bd39d", "source_id": "calculus-df98332989bf699bd39d", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 32*x*exp(2*x**2 + 15) with respect to x.", "answer": "8*exp(2*x**2 + 15)", "expr": "32*x*exp(2*x**2 + 15)", "primitive": "8*exp(2*x**2 + 15)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 7*(6*x - 6)*cos(9*x + 23) - 63*(3*x**2 - 6*x - 6)*sin(9*x + 23) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 7*(3*x**2 - 6*x - 6)*cos(9*x + 23)", "id": "calculus-L2-a8b195a6b1c669c0754f", "source_id": "calculus-a8b195a6b1c669c0754f", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 7*(6*x - 6)*cos(9*x + 23) - 63*(3*x**2 - 6*x - 6)*sin(9*x + 23) with respect to x.", "answer": "7*(3*x**2 - 6*x - 6)*cos(9*x + 23)", "expr": "7*(6*x - 6)*cos(9*x + 23) - 63*(3*x**2 - 6*x - 6)*sin(9*x + 23)", "primitive": "7*(3*x**2 - 6*x - 6)*cos(9*x + 23)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 72*x*exp(6*x**2 + 16) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 6*exp(6*x**2 + 16)", "id": "calculus-L2-c163ccf31c0149531838", "source_id": "calculus-c163ccf31c0149531838", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 72*x*exp(6*x**2 + 16) with respect to x.", "answer": "6*exp(6*x**2 + 16)", "expr": "72*x*exp(6*x**2 + 16)", "primitive": "6*exp(6*x**2 + 16)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (30*exp(x) + 7)*(27*exp(6*x) + 22) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 162*(30*exp(x) + 7)*exp(6*x) + 30*(27*exp(6*x) + 22)*exp(x)", "id": "calculus-L2-0dab7f6bbbab84edbf32", "source_id": "calculus-0dab7f6bbbab84edbf32", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (30*exp(x) + 7)*(27*exp(6*x) + 22) with respect to x.", "answer": "162*(30*exp(x) + 7)*exp(6*x) + 30*(27*exp(6*x) + 22)*exp(x)", "expr": "(30*exp(x) + 7)*(27*exp(6*x) + 22)", "primitive": "(30*exp(x) + 7)*(27*exp(6*x) + 22)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 208*log(9*x + 8)*sin(5*x + 2) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 1040*log(9*x + 8)*cos(5*x + 2) + 1872*sin(5*x + 2)/(9*x + 8)", "id": "calculus-L2-cf9cbc6d6a04f0ee510f", "source_id": "calculus-cf9cbc6d6a04f0ee510f", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 208*log(9*x + 8)*sin(5*x + 2) with respect to x.", "answer": "1040*log(9*x + 8)*cos(5*x + 2) + 1872*sin(5*x + 2)/(9*x + 8)", "expr": "208*log(9*x + 8)*sin(5*x + 2)", "primitive": "208*log(9*x + 8)*sin(5*x + 2)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (-2*x**3 + 4*x + 7)/(x**2 + 10) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(-2*x**3 + 4*x + 7)/(x**2 + 10)**2 + (4 - 6*x**2)/(x**2 + 10)", "id": "calculus-L2-6c0ab0d4dc38a7a4c4b7", "source_id": "calculus-6c0ab0d4dc38a7a4c4b7", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (-2*x**3 + 4*x + 7)/(x**2 + 10) with respect to x.", "answer": "-2*x*(-2*x**3 + 4*x + 7)/(x**2 + 10)**2 + (4 - 6*x**2)/(x**2 + 10)", "expr": "(-2*x**3 + 4*x + 7)/(x**2 + 10)", "primitive": "(-2*x**3 + 4*x + 7)/(x**2 + 10)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 2730*exp(7*x)*log(2*x + 12) + 60*(13*exp(7*x) + 10)/(2*x + 12) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 30*(13*exp(7*x) + 10)*log(2*x + 12)", "id": "calculus-L2-35224cfd7297f68e74cc", "source_id": "calculus-35224cfd7297f68e74cc", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 2730*exp(7*x)*log(2*x + 12) + 60*(13*exp(7*x) + 10)/(2*x + 12) with respect to x.", "answer": "30*(13*exp(7*x) + 10)*log(2*x + 12)", "expr": "2730*exp(7*x)*log(2*x + 12) + 60*(13*exp(7*x) + 10)/(2*x + 12)", "primitive": "30*(13*exp(7*x) + 10)*log(2*x + 12)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (9*x**2 + 2*x + 4)/(x**2 + 6) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(9*x**2 + 2*x + 4)/(x**2 + 6)**2 + (18*x + 2)/(x**2 + 6)", "id": "calculus-L2-316725b3c5efc955d209", "source_id": "calculus-316725b3c5efc955d209", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (9*x**2 + 2*x + 4)/(x**2 + 6) with respect to x.", "answer": "-2*x*(9*x**2 + 2*x + 4)/(x**2 + 6)**2 + (18*x + 2)/(x**2 + 6)", "expr": "(9*x**2 + 2*x + 4)/(x**2 + 6)", "primitive": "(9*x**2 + 2*x + 4)/(x**2 + 6)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(-5*x - 9)/(x**2 + 1)**2 - 5/(x**2 + 1) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (-5*x - 9)/(x**2 + 1)", "id": "calculus-L2-d18c8b05e70dcfb75b4f", "source_id": "calculus-d18c8b05e70dcfb75b4f", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(-5*x - 9)/(x**2 + 1)**2 - 5/(x**2 + 1) with respect to x.", "answer": "(-5*x - 9)/(x**2 + 1)", "expr": "-2*x*(-5*x - 9)/(x**2 + 1)**2 - 5/(x**2 + 1)", "primitive": "(-5*x - 9)/(x**2 + 1)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (4*x**3 - 3*x**2 + 2*x - 7)/(x**2 + 8) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(4*x**3 - 3*x**2 + 2*x - 7)/(x**2 + 8)**2 + (12*x**2 - 6*x + 2)/(x**2 + 8)", "id": "calculus-L2-a2513343e8e95445856f", "source_id": "calculus-a2513343e8e95445856f", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (4*x**3 - 3*x**2 + 2*x - 7)/(x**2 + 8) with respect to x.", "answer": "-2*x*(4*x**3 - 3*x**2 + 2*x - 7)/(x**2 + 8)**2 + (12*x**2 - 6*x + 2)/(x**2 + 8)", "expr": "(4*x**3 - 3*x**2 + 2*x - 7)/(x**2 + 8)", "primitive": "(4*x**3 - 3*x**2 + 2*x - 7)/(x**2 + 8)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -210*(7*exp(11*x) + 19)*sin(10*x + 12) + 1617*exp(11*x)*cos(10*x + 12) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 21*(7*exp(11*x) + 19)*cos(10*x + 12)", "id": "calculus-L2-8ff3093809a91d30123d", "source_id": "calculus-8ff3093809a91d30123d", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -210*(7*exp(11*x) + 19)*sin(10*x + 12) + 1617*exp(11*x)*cos(10*x + 12) with respect to x.", "answer": "21*(7*exp(11*x) + 19)*cos(10*x + 12)", "expr": "-210*(7*exp(11*x) + 19)*sin(10*x + 12) + 1617*exp(11*x)*cos(10*x + 12)", "primitive": "21*(7*exp(11*x) + 19)*cos(10*x + 12)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 27*(x**4 - 8*x**3 - 7*x**2 + 5*x - 6)*cos(10*x + 20) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 27*(4*x**3 - 24*x**2 - 14*x + 5)*cos(10*x + 20) - 270*(x**4 - 8*x**3 - 7*x**2 + 5*x - 6)*sin(10*x + 20)", "id": "calculus-L2-d3298e895be72a215ca3", "source_id": "calculus-d3298e895be72a215ca3", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 27*(x**4 - 8*x**3 - 7*x**2 + 5*x - 6)*cos(10*x + 20) with respect to x.", "answer": "27*(4*x**3 - 24*x**2 - 14*x + 5)*cos(10*x + 20) - 270*(x**4 - 8*x**3 - 7*x**2 + 5*x - 6)*sin(10*x + 20)", "expr": "27*(x**4 - 8*x**3 - 7*x**2 + 5*x - 6)*cos(10*x + 20)", "primitive": "27*(x**4 - 8*x**3 - 7*x**2 + 5*x - 6)*cos(10*x + 20)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 13*(3*x**4 + 2*x**3 - 8*x**2 + 8*x - 5)*cos(4*x + 14) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 13*(12*x**3 + 6*x**2 - 16*x + 8)*cos(4*x + 14) - 52*(3*x**4 + 2*x**3 - 8*x**2 + 8*x - 5)*sin(4*x + 14)", "id": "calculus-L2-70b3fa131462c55cbd77", "source_id": "calculus-70b3fa131462c55cbd77", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 13*(3*x**4 + 2*x**3 - 8*x**2 + 8*x - 5)*cos(4*x + 14) with respect to x.", "answer": "13*(12*x**3 + 6*x**2 - 16*x + 8)*cos(4*x + 14) - 52*(3*x**4 + 2*x**3 - 8*x**2 + 8*x - 5)*sin(4*x + 14)", "expr": "13*(3*x**4 + 2*x**3 - 8*x**2 + 8*x - 5)*cos(4*x + 14)", "primitive": "13*(3*x**4 + 2*x**3 - 8*x**2 + 8*x - 5)*cos(4*x + 14)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(8*x - 3)/(x**2 + 20)**2 + 8/(x**2 + 20) with respect to x from 0 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 507/580", "id": "calculus-L2-1182b43f9087da755108", "source_id": "calculus-1182b43f9087da755108", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(8*x - 3)/(x**2 + 20)**2 + 8/(x**2 + 20) with respect to x from 0 to 3.", "answer": "507/580", "expr": "-2*x*(8*x - 3)/(x**2 + 20)**2 + 8/(x**2 + 20)", "primitive": "(8*x - 3)/(x**2 + 20)", "lower": "0", "upper": "3", "split": "dev"}
{"instruction": "Evaluate the definite integral of -546*sin(2*x + 25)*sin(7*x + 25) + 156*cos(2*x + 25)*cos(7*x + 25) with respect to x from 1 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -78*sin(27)*cos(32) + 78*sin(31)*cos(46)", "id": "calculus-L2-fd97c1c4de03390c8176", "source_id": "calculus-fd97c1c4de03390c8176", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -546*sin(2*x + 25)*sin(7*x + 25) + 156*cos(2*x + 25)*cos(7*x + 25) with respect to x from 1 to 3.", "answer": "-78*sin(27)*cos(32) + 78*sin(31)*cos(46)", "expr": "-546*sin(2*x + 25)*sin(7*x + 25) + 156*cos(2*x + 25)*cos(7*x + 25)", "primitive": "78*sin(2*x + 25)*cos(7*x + 25)", "lower": "1", "upper": "3", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (-3*x**3 + x**2 - 2*x + 7)/(x**2 + 5) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(-3*x**3 + x**2 - 2*x + 7)/(x**2 + 5)**2 + (-9*x**2 + 2*x - 2)/(x**2 + 5)", "id": "calculus-L2-fcd2677713719f8648bd", "source_id": "calculus-fcd2677713719f8648bd", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (-3*x**3 + x**2 - 2*x + 7)/(x**2 + 5) with respect to x.", "answer": "-2*x*(-3*x**3 + x**2 - 2*x + 7)/(x**2 + 5)**2 + (-9*x**2 + 2*x - 2)/(x**2 + 5)", "expr": "(-3*x**3 + x**2 - 2*x + 7)/(x**2 + 5)", "primitive": "(-3*x**3 + x**2 - 2*x + 7)/(x**2 + 5)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 5*(3 - 2*x)*sin(11*x + 12) + 55*(-x**2 + 3*x - 3)*cos(11*x + 12) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 5*(-x**2 + 3*x - 3)*sin(11*x + 12)", "id": "calculus-L2-19adaa3dfd1dbb1529c9", "source_id": "calculus-19adaa3dfd1dbb1529c9", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 5*(3 - 2*x)*sin(11*x + 12) + 55*(-x**2 + 3*x - 3)*cos(11*x + 12) with respect to x.", "answer": "5*(-x**2 + 3*x - 3)*sin(11*x + 12)", "expr": "5*(3 - 2*x)*sin(11*x + 12) + 55*(-x**2 + 3*x - 3)*cos(11*x + 12)", "primitive": "5*(-x**2 + 3*x - 3)*sin(11*x + 12)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 208*x*exp(8*x**2 + 16) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 13*exp(8*x**2 + 16)", "id": "calculus-L2-d90f354cf9a66373afc0", "source_id": "calculus-d90f354cf9a66373afc0", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 208*x*exp(8*x**2 + 16) with respect to x.", "answer": "13*exp(8*x**2 + 16)", "expr": "208*x*exp(8*x**2 + 16)", "primitive": "13*exp(8*x**2 + 16)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -15*sin(2*x)*sin(15*x) + 2*cos(2*x)*cos(15*x) with respect to x from 1 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: sin(6)*cos(45) - sin(2)*cos(15)", "id": "calculus-L2-f8ccb8bda571fa08eced", "source_id": "calculus-f8ccb8bda571fa08eced", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -15*sin(2*x)*sin(15*x) + 2*cos(2*x)*cos(15*x) with respect to x from 1 to 3.", "answer": "sin(6)*cos(45) - sin(2)*cos(15)", "expr": "-15*sin(2*x)*sin(15*x) + 2*cos(2*x)*cos(15*x)", "primitive": "sin(2*x)*cos(15*x)", "lower": "1", "upper": "3", "split": "dev"}
{"instruction": "Find the derivative of f(x) = sin(8*x)*cos(17*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -17*sin(8*x)*sin(17*x) + 8*cos(8*x)*cos(17*x)", "id": "calculus-L2-9a24c24efbaf01d17e21", "source_id": "calculus-9a24c24efbaf01d17e21", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = sin(8*x)*cos(17*x) with respect to x.", "answer": "-17*sin(8*x)*sin(17*x) + 8*cos(8*x)*cos(17*x)", "expr": "sin(8*x)*cos(17*x)", "primitive": "sin(8*x)*cos(17*x)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 192*x*exp(6*x**2 + 12) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 16*exp(6*x**2 + 12)", "id": "calculus-L2-30771467261c96a1eba4", "source_id": "calculus-30771467261c96a1eba4", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 192*x*exp(6*x**2 + 12) with respect to x.", "answer": "16*exp(6*x**2 + 12)", "expr": "192*x*exp(6*x**2 + 12)", "primitive": "16*exp(6*x**2 + 12)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 140*(22*exp(2*x) + 29)*exp(5*x) + 44*(28*exp(5*x) + 29)*exp(2*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (22*exp(2*x) + 29)*(28*exp(5*x) + 29)", "id": "calculus-L2-febe0550c591f266aace", "source_id": "calculus-febe0550c591f266aace", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 140*(22*exp(2*x) + 29)*exp(5*x) + 44*(28*exp(5*x) + 29)*exp(2*x) with respect to x.", "answer": "(22*exp(2*x) + 29)*(28*exp(5*x) + 29)", "expr": "140*(22*exp(2*x) + 29)*exp(5*x) + 44*(28*exp(5*x) + 29)*exp(2*x)", "primitive": "(22*exp(2*x) + 29)*(28*exp(5*x) + 29)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 23*(5*x**2 - 5*x + 6)*sin(11*x + 28) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 23*(10*x - 5)*sin(11*x + 28) + 253*(5*x**2 - 5*x + 6)*cos(11*x + 28)", "id": "calculus-L2-c6ffebd345501f9a77d1", "source_id": "calculus-c6ffebd345501f9a77d1", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 23*(5*x**2 - 5*x + 6)*sin(11*x + 28) with respect to x.", "answer": "23*(10*x - 5)*sin(11*x + 28) + 253*(5*x**2 - 5*x + 6)*cos(11*x + 28)", "expr": "23*(5*x**2 - 5*x + 6)*sin(11*x + 28)", "primitive": "23*(5*x**2 - 5*x + 6)*sin(11*x + 28)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 20*exp(4*x**2 + 19) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 160*x*exp(4*x**2 + 19)", "id": "calculus-L2-f8536211259a529037be", "source_id": "calculus-f8536211259a529037be", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 20*exp(4*x**2 + 19) with respect to x.", "answer": "160*x*exp(4*x**2 + 19)", "expr": "20*exp(4*x**2 + 19)", "primitive": "20*exp(4*x**2 + 19)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(5*x**3 + 3*x**2 - 2*x - 8)/(x**2 + 3)**2 + (15*x**2 + 6*x - 2)/(x**2 + 3) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (5*x**3 + 3*x**2 - 2*x - 8)/(x**2 + 3)", "id": "calculus-L2-bcd43d2f0a901659ddaf", "source_id": "calculus-bcd43d2f0a901659ddaf", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(5*x**3 + 3*x**2 - 2*x - 8)/(x**2 + 3)**2 + (15*x**2 + 6*x - 2)/(x**2 + 3) with respect to x.", "answer": "(5*x**3 + 3*x**2 - 2*x - 8)/(x**2 + 3)", "expr": "-2*x*(5*x**3 + 3*x**2 - 2*x - 8)/(x**2 + 3)**2 + (15*x**2 + 6*x - 2)/(x**2 + 3)", "primitive": "(5*x**3 + 3*x**2 - 2*x - 8)/(x**2 + 3)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(4*x**3 - 7*x**2 + 8*x - 1)/(x**2 + 8)**2 + (12*x**2 - 14*x + 8)/(x**2 + 8) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (4*x**3 - 7*x**2 + 8*x - 1)/(x**2 + 8)", "id": "calculus-L2-a304f47e5ac01a707a19", "source_id": "calculus-a304f47e5ac01a707a19", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(4*x**3 - 7*x**2 + 8*x - 1)/(x**2 + 8)**2 + (12*x**2 - 14*x + 8)/(x**2 + 8) with respect to x.", "answer": "(4*x**3 - 7*x**2 + 8*x - 1)/(x**2 + 8)", "expr": "-2*x*(4*x**3 - 7*x**2 + 8*x - 1)/(x**2 + 8)**2 + (12*x**2 - 14*x + 8)/(x**2 + 8)", "primitive": "(4*x**3 - 7*x**2 + 8*x - 1)/(x**2 + 8)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -6728*log(6*x + 22)*sin(8*x + 5) + 5046*cos(8*x + 5)/(6*x + 22) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 841*log(6*x + 22)*cos(8*x + 5)", "id": "calculus-L2-bdc324362c16fc4c83db", "source_id": "calculus-bdc324362c16fc4c83db", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -6728*log(6*x + 22)*sin(8*x + 5) + 5046*cos(8*x + 5)/(6*x + 22) with respect to x.", "answer": "841*log(6*x + 22)*cos(8*x + 5)", "expr": "-6728*log(6*x + 22)*sin(8*x + 5) + 5046*cos(8*x + 5)/(6*x + 22)", "primitive": "841*log(6*x + 22)*cos(8*x + 5)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -8*sin(6*x)*sin(8*x) + 6*cos(6*x)*cos(8*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: sin(6*x)*cos(8*x)", "id": "calculus-L2-266fc6f7bdcdca65a860", "source_id": "calculus-266fc6f7bdcdca65a860", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -8*sin(6*x)*sin(8*x) + 6*cos(6*x)*cos(8*x) with respect to x.", "answer": "sin(6*x)*cos(8*x)", "expr": "-8*sin(6*x)*sin(8*x) + 6*cos(6*x)*cos(8*x)", "primitive": "sin(6*x)*cos(8*x)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(-4*x**2 - 4*x - 7)/(x**2 + 15)**2 + (-8*x - 4)/(x**2 + 15) with respect to x from 1 to 2. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -211/304", "id": "calculus-L2-3411d80b8c3c89fdd5a1", "source_id": "calculus-3411d80b8c3c89fdd5a1", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(-4*x**2 - 4*x - 7)/(x**2 + 15)**2 + (-8*x - 4)/(x**2 + 15) with respect to x from 1 to 2.", "answer": "-211/304", "expr": "-2*x*(-4*x**2 - 4*x - 7)/(x**2 + 15)**2 + (-8*x - 4)/(x**2 + 15)", "primitive": "(-4*x**2 - 4*x - 7)/(x**2 + 15)", "lower": "1", "upper": "2", "split": "dev"}
{"instruction": "Evaluate the definite integral of -294*sin(x + 19)*cos(10*x + 23) - 2940*sin(10*x + 23)*cos(x + 19) with respect to x from 0 to 2. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 294*cos(21)*cos(43) - 294*cos(19)*cos(23)", "id": "calculus-L2-8eb619a2c5661452e2c6", "source_id": "calculus-8eb619a2c5661452e2c6", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -294*sin(x + 19)*cos(10*x + 23) - 2940*sin(10*x + 23)*cos(x + 19) with respect to x from 0 to 2.", "answer": "294*cos(21)*cos(43) - 294*cos(19)*cos(23)", "expr": "-294*sin(x + 19)*cos(10*x + 23) - 2940*sin(10*x + 23)*cos(x + 19)", "primitive": "294*cos(x + 19)*cos(10*x + 23)", "lower": "0", "upper": "2", "split": "dev"}
{"instruction": "Evaluate the definite integral of -4*sin(4*x)*sin(5*x) + 5*cos(4*x)*cos(5*x) with respect to x from 0 to 2. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: sin(10)*cos(8)", "id": "calculus-L2-b780c5fa31437a144540", "source_id": "calculus-b780c5fa31437a144540", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -4*sin(4*x)*sin(5*x) + 5*cos(4*x)*cos(5*x) with respect to x from 0 to 2.", "answer": "sin(10)*cos(8)", "expr": "-4*sin(4*x)*sin(5*x) + 5*cos(4*x)*cos(5*x)", "primitive": "sin(5*x)*cos(4*x)", "lower": "0", "upper": "2", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(-5*x**3 - 9*x**2 - 7*x - 7)/(x**2 + 19)**2 + (-15*x**2 - 18*x - 7)/(x**2 + 19) with respect to x from 2 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -724/161", "id": "calculus-L2-ec5d87db8955bc6ffcd3", "source_id": "calculus-ec5d87db8955bc6ffcd3", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(-5*x**3 - 9*x**2 - 7*x - 7)/(x**2 + 19)**2 + (-15*x**2 - 18*x - 7)/(x**2 + 19) with respect to x from 2 to 3.", "answer": "-724/161", "expr": "-2*x*(-5*x**3 - 9*x**2 - 7*x - 7)/(x**2 + 19)**2 + (-15*x**2 - 18*x - 7)/(x**2 + 19)", "primitive": "(-5*x**3 - 9*x**2 - 7*x - 7)/(x**2 + 19)", "lower": "2", "upper": "3", "split": "dev"}
{"instruction": "Find an antiderivative of 2*x*exp(x**2 + 10) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: exp(x**2 + 10)", "id": "calculus-L2-49e05f7db53a6e1d7a71", "source_id": "calculus-49e05f7db53a6e1d7a71", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 2*x*exp(x**2 + 10) with respect to x.", "answer": "exp(x**2 + 10)", "expr": "2*x*exp(x**2 + 10)", "primitive": "exp(x**2 + 10)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of (27*exp(5*x) + 12)*(8*x**3 + 6*x**2 + 10*x - 8) + 135*(2*x**4 + 2*x**3 + 5*x**2 - 8*x + 8)*exp(5*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (27*exp(5*x) + 12)*(2*x**4 + 2*x**3 + 5*x**2 - 8*x + 8)", "id": "calculus-L2-067e53daef1d51b51369", "source_id": "calculus-067e53daef1d51b51369", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of (27*exp(5*x) + 12)*(8*x**3 + 6*x**2 + 10*x - 8) + 135*(2*x**4 + 2*x**3 + 5*x**2 - 8*x + 8)*exp(5*x) with respect to x.", "answer": "(27*exp(5*x) + 12)*(2*x**4 + 2*x**3 + 5*x**2 - 8*x + 8)", "expr": "(27*exp(5*x) + 12)*(8*x**3 + 6*x**2 + 10*x - 8) + 135*(2*x**4 + 2*x**3 + 5*x**2 - 8*x + 8)*exp(5*x)", "primitive": "(27*exp(5*x) + 12)*(2*x**4 + 2*x**3 + 5*x**2 - 8*x + 8)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 10*exp(7*x**2 + 11) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 140*x*exp(7*x**2 + 11)", "id": "calculus-L2-0bbf482af7c88174f9d8", "source_id": "calculus-0bbf482af7c88174f9d8", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 10*exp(7*x**2 + 11) with respect to x.", "answer": "140*x*exp(7*x**2 + 11)", "expr": "10*exp(7*x**2 + 11)", "primitive": "10*exp(7*x**2 + 11)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (17*exp(4*x) + 21)*(16*exp(8*x) + 4) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 128*(17*exp(4*x) + 21)*exp(8*x) + 68*(16*exp(8*x) + 4)*exp(4*x)", "id": "calculus-L2-dee9adad63cd4c835394", "source_id": "calculus-dee9adad63cd4c835394", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (17*exp(4*x) + 21)*(16*exp(8*x) + 4) with respect to x.", "answer": "128*(17*exp(4*x) + 21)*exp(8*x) + 68*(16*exp(8*x) + 4)*exp(4*x)", "expr": "(17*exp(4*x) + 21)*(16*exp(8*x) + 4)", "primitive": "(17*exp(4*x) + 21)*(16*exp(8*x) + 4)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(7*x - 4)/(x**2 + 12)**2 + 7/(x**2 + 12) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (7*x - 4)/(x**2 + 12)", "id": "calculus-L2-457bb017a5c07f916e33", "source_id": "calculus-457bb017a5c07f916e33", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(7*x - 4)/(x**2 + 12)**2 + 7/(x**2 + 12) with respect to x.", "answer": "(7*x - 4)/(x**2 + 12)", "expr": "-2*x*(7*x - 4)/(x**2 + 12)**2 + 7/(x**2 + 12)", "primitive": "(7*x - 4)/(x**2 + 12)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (9*x**3 - 5*x**2 - 8*x + 7)/(x**2 + 13) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(9*x**3 - 5*x**2 - 8*x + 7)/(x**2 + 13)**2 + (27*x**2 - 10*x - 8)/(x**2 + 13)", "id": "calculus-L2-2022bbcbacbbd194093a", "source_id": "calculus-2022bbcbacbbd194093a", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (9*x**3 - 5*x**2 - 8*x + 7)/(x**2 + 13) with respect to x.", "answer": "-2*x*(9*x**3 - 5*x**2 - 8*x + 7)/(x**2 + 13)**2 + (27*x**2 - 10*x - 8)/(x**2 + 13)", "expr": "(9*x**3 - 5*x**2 - 8*x + 7)/(x**2 + 13)", "primitive": "(9*x**3 - 5*x**2 - 8*x + 7)/(x**2 + 13)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 11*(11*exp(x) + 21)*sin(10*x + 26) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 110*(11*exp(x) + 21)*cos(10*x + 26) + 121*exp(x)*sin(10*x + 26)", "id": "calculus-L2-4108714a272655bec399", "source_id": "calculus-4108714a272655bec399", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 11*(11*exp(x) + 21)*sin(10*x + 26) with respect to x.", "answer": "110*(11*exp(x) + 21)*cos(10*x + 26) + 121*exp(x)*sin(10*x + 26)", "expr": "11*(11*exp(x) + 21)*sin(10*x + 26)", "primitive": "11*(11*exp(x) + 21)*sin(10*x + 26)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(-4*x**2 - 4*x - 1)/(x**2 + 17)**2 + (-8*x - 4)/(x**2 + 17) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (-4*x**2 - 4*x - 1)/(x**2 + 17)", "id": "calculus-L2-6da2e17131afba95fd88", "source_id": "calculus-6da2e17131afba95fd88", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(-4*x**2 - 4*x - 1)/(x**2 + 17)**2 + (-8*x - 4)/(x**2 + 17) with respect to x.", "answer": "(-4*x**2 - 4*x - 1)/(x**2 + 17)", "expr": "-2*x*(-4*x**2 - 4*x - 1)/(x**2 + 17)**2 + (-8*x - 4)/(x**2 + 17)", "primitive": "(-4*x**2 - 4*x - 1)/(x**2 + 17)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 156*log(12*x + 7)*sin(3*x + 26) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 468*log(12*x + 7)*cos(3*x + 26) + 1872*sin(3*x + 26)/(12*x + 7)", "id": "calculus-L2-fa46f87e6491b0a664ed", "source_id": "calculus-fa46f87e6491b0a664ed", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 156*log(12*x + 7)*sin(3*x + 26) with respect to x.", "answer": "468*log(12*x + 7)*cos(3*x + 26) + 1872*sin(3*x + 26)/(12*x + 7)", "expr": "156*log(12*x + 7)*sin(3*x + 26)", "primitive": "156*log(12*x + 7)*sin(3*x + 26)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(7*x**3 - 6*x**2 + 5*x + 5)/(x**2 + 16)**2 + (21*x**2 - 12*x + 5)/(x**2 + 16) with respect to x from 0 to 1. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 91/272", "id": "calculus-L2-8211ac6e51c9a9c87ac5", "source_id": "calculus-8211ac6e51c9a9c87ac5", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(7*x**3 - 6*x**2 + 5*x + 5)/(x**2 + 16)**2 + (21*x**2 - 12*x + 5)/(x**2 + 16) with respect to x from 0 to 1.", "answer": "91/272", "expr": "-2*x*(7*x**3 - 6*x**2 + 5*x + 5)/(x**2 + 16)**2 + (21*x**2 - 12*x + 5)/(x**2 + 16)", "primitive": "(7*x**3 - 6*x**2 + 5*x + 5)/(x**2 + 16)", "lower": "0", "upper": "1", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (3 - 7*x)/(x**2 + 2) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(3 - 7*x)/(x**2 + 2)**2 - 7/(x**2 + 2)", "id": "calculus-L2-5ecaca20b67102f87391", "source_id": "calculus-5ecaca20b67102f87391", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (3 - 7*x)/(x**2 + 2) with respect to x.", "answer": "-2*x*(3 - 7*x)/(x**2 + 2)**2 - 7/(x**2 + 2)", "expr": "(3 - 7*x)/(x**2 + 2)", "primitive": "(3 - 7*x)/(x**2 + 2)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (5*x**3 + 7*x**2 + 7*x)/(x**2 + 1) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(5*x**3 + 7*x**2 + 7*x)/(x**2 + 1)**2 + (15*x**2 + 14*x + 7)/(x**2 + 1)", "id": "calculus-L2-08f5458308b971637a49", "source_id": "calculus-08f5458308b971637a49", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (5*x**3 + 7*x**2 + 7*x)/(x**2 + 1) with respect to x.", "answer": "-2*x*(5*x**3 + 7*x**2 + 7*x)/(x**2 + 1)**2 + (15*x**2 + 14*x + 7)/(x**2 + 1)", "expr": "(5*x**3 + 7*x**2 + 7*x)/(x**2 + 1)", "primitive": "(5*x**3 + 7*x**2 + 7*x)/(x**2 + 1)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 4*(4*x**3 + 8*x**2 - 6*x - 5)*cos(5*x + 14) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 4*(12*x**2 + 16*x - 6)*cos(5*x + 14) - 20*(4*x**3 + 8*x**2 - 6*x - 5)*sin(5*x + 14)", "id": "calculus-L2-c50625105f773fcf3894", "source_id": "calculus-c50625105f773fcf3894", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 4*(4*x**3 + 8*x**2 - 6*x - 5)*cos(5*x + 14) with respect to x.", "answer": "4*(12*x**2 + 16*x - 6)*cos(5*x + 14) - 20*(4*x**3 + 8*x**2 - 6*x - 5)*sin(5*x + 14)", "expr": "4*(4*x**3 + 8*x**2 - 6*x - 5)*cos(5*x + 14)", "primitive": "4*(4*x**3 + 8*x**2 - 6*x - 5)*cos(5*x + 14)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(x**2 - 2*x - 4)/(x**2 + 3)**2 + (2*x - 2)/(x**2 + 3) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (x**2 - 2*x - 4)/(x**2 + 3)", "id": "calculus-L2-e05d9957baf418fa132a", "source_id": "calculus-e05d9957baf418fa132a", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(x**2 - 2*x - 4)/(x**2 + 3)**2 + (2*x - 2)/(x**2 + 3) with respect to x.", "answer": "(x**2 - 2*x - 4)/(x**2 + 3)", "expr": "-2*x*(x**2 - 2*x - 4)/(x**2 + 3)**2 + (2*x - 2)/(x**2 + 3)", "primitive": "(x**2 - 2*x - 4)/(x**2 + 3)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (2*x**3 - 3*x**2 + 7*x + 3)/(x**2 + 19) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(2*x**3 - 3*x**2 + 7*x + 3)/(x**2 + 19)**2 + (6*x**2 - 6*x + 7)/(x**2 + 19)", "id": "calculus-L2-7e2713471ff172b86308", "source_id": "calculus-7e2713471ff172b86308", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (2*x**3 - 3*x**2 + 7*x + 3)/(x**2 + 19) with respect to x.", "answer": "-2*x*(2*x**3 - 3*x**2 + 7*x + 3)/(x**2 + 19)**2 + (6*x**2 - 6*x + 7)/(x**2 + 19)", "expr": "(2*x**3 - 3*x**2 + 7*x + 3)/(x**2 + 19)", "primitive": "(2*x**3 - 3*x**2 + 7*x + 3)/(x**2 + 19)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of 672*log(3*x + 26)*cos(2*x + 13) + 1008*sin(2*x + 13)/(3*x + 26) with respect to x from 0 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -336*log(26)*sin(13) + 336*log(35)*sin(19)", "id": "calculus-L2-b9505fdae2239c45f4f6", "source_id": "calculus-b9505fdae2239c45f4f6", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of 672*log(3*x + 26)*cos(2*x + 13) + 1008*sin(2*x + 13)/(3*x + 26) with respect to x from 0 to 3.", "answer": "-336*log(26)*sin(13) + 336*log(35)*sin(19)", "expr": "672*log(3*x + 26)*cos(2*x + 13) + 1008*sin(2*x + 13)/(3*x + 26)", "primitive": "336*log(3*x + 26)*sin(2*x + 13)", "lower": "0", "upper": "3", "split": "dev"}
{"instruction": "Find the derivative of f(x) = sin(8*x)*cos(4*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -4*sin(4*x)*sin(8*x) + 8*cos(4*x)*cos(8*x)", "id": "calculus-L2-5329d380b47fe09ddfcc", "source_id": "calculus-5329d380b47fe09ddfcc", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = sin(8*x)*cos(4*x) with respect to x.", "answer": "-4*sin(4*x)*sin(8*x) + 8*cos(4*x)*cos(8*x)", "expr": "sin(8*x)*cos(4*x)", "primitive": "sin(8*x)*cos(4*x)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(9*x**2 - 5*x - 7)/(x**2 + 8)**2 + (18*x - 5)/(x**2 + 8) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (9*x**2 - 5*x - 7)/(x**2 + 8)", "id": "calculus-L2-1b91f5da564c3237540b", "source_id": "calculus-1b91f5da564c3237540b", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(9*x**2 - 5*x - 7)/(x**2 + 8)**2 + (18*x - 5)/(x**2 + 8) with respect to x.", "answer": "(9*x**2 - 5*x - 7)/(x**2 + 8)", "expr": "-2*x*(9*x**2 - 5*x - 7)/(x**2 + 8)**2 + (18*x - 5)/(x**2 + 8)", "primitive": "(9*x**2 - 5*x - 7)/(x**2 + 8)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (7*x + 4)/(x**2 + 20) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(7*x + 4)/(x**2 + 20)**2 + 7/(x**2 + 20)", "id": "calculus-L2-5014b191311db583268e", "source_id": "calculus-5014b191311db583268e", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (7*x + 4)/(x**2 + 20) with respect to x.", "answer": "-2*x*(7*x + 4)/(x**2 + 20)**2 + 7/(x**2 + 20)", "expr": "(7*x + 4)/(x**2 + 20)", "primitive": "(7*x + 4)/(x**2 + 20)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(9*x + 9)/(x**2 + 2)**2 + 9/(x**2 + 2) with respect to x from 1 to 2. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -3/2", "id": "calculus-L2-0793e873cc095180c569", "source_id": "calculus-0793e873cc095180c569", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(9*x + 9)/(x**2 + 2)**2 + 9/(x**2 + 2) with respect to x from 1 to 2.", "answer": "-3/2", "expr": "-2*x*(9*x + 9)/(x**2 + 2)**2 + 9/(x**2 + 2)", "primitive": "(9*x + 9)/(x**2 + 2)", "lower": "1", "upper": "2", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (-8*x**3 + 6*x**2 - 8*x)/(x**2 + 13) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(-8*x**3 + 6*x**2 - 8*x)/(x**2 + 13)**2 + (-24*x**2 + 12*x - 8)/(x**2 + 13)", "id": "calculus-L2-619a36af4f4a06b97439", "source_id": "calculus-619a36af4f4a06b97439", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (-8*x**3 + 6*x**2 - 8*x)/(x**2 + 13) with respect to x.", "answer": "-2*x*(-8*x**3 + 6*x**2 - 8*x)/(x**2 + 13)**2 + (-24*x**2 + 12*x - 8)/(x**2 + 13)", "expr": "(-8*x**3 + 6*x**2 - 8*x)/(x**2 + 13)", "primitive": "(-8*x**3 + 6*x**2 - 8*x)/(x**2 + 13)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of 4*(-12*x - 3)*sin(4*x + 26) + 16*(-6*x**2 - 3*x - 4)*cos(4*x + 26) with respect to x from 2 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -268*sin(38) + 136*sin(34)", "id": "calculus-L2-2916962ecff9ee4f91d8", "source_id": "calculus-2916962ecff9ee4f91d8", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of 4*(-12*x - 3)*sin(4*x + 26) + 16*(-6*x**2 - 3*x - 4)*cos(4*x + 26) with respect to x from 2 to 3.", "answer": "-268*sin(38) + 136*sin(34)", "expr": "4*(-12*x - 3)*sin(4*x + 26) + 16*(-6*x**2 - 3*x - 4)*cos(4*x + 26)", "primitive": "4*(-6*x**2 - 3*x - 4)*sin(4*x + 26)", "lower": "2", "upper": "3", "split": "dev"}
{"instruction": "Evaluate the definite integral of -9*sin(5*x)*sin(9*x) + 5*cos(5*x)*cos(9*x) with respect to x from 2 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: sin(15)*cos(27) - sin(10)*cos(18)", "id": "calculus-L2-6f6b3b6c4d3db3f72edb", "source_id": "calculus-6f6b3b6c4d3db3f72edb", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -9*sin(5*x)*sin(9*x) + 5*cos(5*x)*cos(9*x) with respect to x from 2 to 3.", "answer": "sin(15)*cos(27) - sin(10)*cos(18)", "expr": "-9*sin(5*x)*sin(9*x) + 5*cos(5*x)*cos(9*x)", "primitive": "sin(5*x)*cos(9*x)", "lower": "2", "upper": "3", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (3 - 3*x**2)/(x**2 + 7) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(3 - 3*x**2)/(x**2 + 7)**2 - 6*x/(x**2 + 7)", "id": "calculus-L2-417d6aa87c3bae1864e8", "source_id": "calculus-417d6aa87c3bae1864e8", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (3 - 3*x**2)/(x**2 + 7) with respect to x.", "answer": "-2*x*(3 - 3*x**2)/(x**2 + 7)**2 - 6*x/(x**2 + 7)", "expr": "(3 - 3*x**2)/(x**2 + 7)", "primitive": "(3 - 3*x**2)/(x**2 + 7)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 8*exp(9*x**2 + 15) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 144*x*exp(9*x**2 + 15)", "id": "calculus-L2-bf5f1a5bdad12d13ca23", "source_id": "calculus-bf5f1a5bdad12d13ca23", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 8*exp(9*x**2 + 15) with respect to x.", "answer": "144*x*exp(9*x**2 + 15)", "expr": "8*exp(9*x**2 + 15)", "primitive": "8*exp(9*x**2 + 15)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (5*x + 2)/(x**2 + 16) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(5*x + 2)/(x**2 + 16)**2 + 5/(x**2 + 16)", "id": "calculus-L2-aa5414c7fa94a98a3a1e", "source_id": "calculus-aa5414c7fa94a98a3a1e", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (5*x + 2)/(x**2 + 16) with respect to x.", "answer": "-2*x*(5*x + 2)/(x**2 + 16)**2 + 5/(x**2 + 16)", "expr": "(5*x + 2)/(x**2 + 16)", "primitive": "(5*x + 2)/(x**2 + 16)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 40*x*exp(x**2 + 2) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 20*exp(x**2 + 2)", "id": "calculus-L2-41fd78b9665cf7a6c513", "source_id": "calculus-41fd78b9665cf7a6c513", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 40*x*exp(x**2 + 2) with respect to x.", "answer": "20*exp(x**2 + 2)", "expr": "40*x*exp(x**2 + 2)", "primitive": "20*exp(x**2 + 2)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 1210*log(3*x + 16)/(11*x + 28) + 330*log(11*x + 28)/(3*x + 16) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 110*log(3*x + 16)*log(11*x + 28)", "id": "calculus-L2-a1559d4c7b71fb8335b3", "source_id": "calculus-a1559d4c7b71fb8335b3", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 1210*log(3*x + 16)/(11*x + 28) + 330*log(11*x + 28)/(3*x + 16) with respect to x.", "answer": "110*log(3*x + 16)*log(11*x + 28)", "expr": "1210*log(3*x + 16)/(11*x + 28) + 330*log(11*x + 28)/(3*x + 16)", "primitive": "110*log(3*x + 16)*log(11*x + 28)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(6*x**2 - 8*x - 6)/(x**2 + 20)**2 + (12*x - 8)/(x**2 + 20) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (6*x**2 - 8*x - 6)/(x**2 + 20)", "id": "calculus-L2-da2c30e9d13a8cff2c17", "source_id": "calculus-da2c30e9d13a8cff2c17", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(6*x**2 - 8*x - 6)/(x**2 + 20)**2 + (12*x - 8)/(x**2 + 20) with respect to x.", "answer": "(6*x**2 - 8*x - 6)/(x**2 + 20)", "expr": "-2*x*(6*x**2 - 8*x - 6)/(x**2 + 20)**2 + (12*x - 8)/(x**2 + 20)", "primitive": "(6*x**2 - 8*x - 6)/(x**2 + 20)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 126*log(12*x + 3)*sin(12*x + 12) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 1512*log(12*x + 3)*cos(12*x + 12) + 1512*sin(12*x + 12)/(12*x + 3)", "id": "calculus-L2-4e19bcc1c10ce57f1626", "source_id": "calculus-4e19bcc1c10ce57f1626", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 126*log(12*x + 3)*sin(12*x + 12) with respect to x.", "answer": "1512*log(12*x + 3)*cos(12*x + 12) + 1512*sin(12*x + 12)/(12*x + 3)", "expr": "126*log(12*x + 3)*sin(12*x + 12)", "primitive": "126*log(12*x + 3)*sin(12*x + 12)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(-4*x**3 - 7*x**2 - 2*x + 9)/(x**2 + 17)**2 + (-12*x**2 - 14*x - 2)/(x**2 + 17) with respect to x from 2 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -1049/273", "id": "calculus-L2-bd4450bd937dde591fad", "source_id": "calculus-bd4450bd937dde591fad", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(-4*x**3 - 7*x**2 - 2*x + 9)/(x**2 + 17)**2 + (-12*x**2 - 14*x - 2)/(x**2 + 17) with respect to x from 2 to 3.", "answer": "-1049/273", "expr": "-2*x*(-4*x**3 - 7*x**2 - 2*x + 9)/(x**2 + 17)**2 + (-12*x**2 - 14*x - 2)/(x**2 + 17)", "primitive": "(-4*x**3 - 7*x**2 - 2*x + 9)/(x**2 + 17)", "lower": "2", "upper": "3", "split": "dev"}
{"instruction": "Find an antiderivative of -1134*sin(6*x + 25)*cos(8*x + 27) - 1512*sin(8*x + 27)*cos(6*x + 25) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 189*cos(6*x + 25)*cos(8*x + 27)", "id": "calculus-L2-69dfb581d234201a6c4c", "source_id": "calculus-69dfb581d234201a6c4c", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -1134*sin(6*x + 25)*cos(8*x + 27) - 1512*sin(8*x + 27)*cos(6*x + 25) with respect to x.", "answer": "189*cos(6*x + 25)*cos(8*x + 27)", "expr": "-1134*sin(6*x + 25)*cos(8*x + 27) - 1512*sin(8*x + 27)*cos(6*x + 25)", "primitive": "189*cos(6*x + 25)*cos(8*x + 27)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of 5*(3*x**2 + 10*x - 2)*cos(12*x + 17) - 60*(x**3 + 5*x**2 - 2*x - 2)*sin(12*x + 17) with respect to x from 1 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 320*cos(53) - 10*cos(29)", "id": "calculus-L2-844862c490163a307da2", "source_id": "calculus-844862c490163a307da2", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of 5*(3*x**2 + 10*x - 2)*cos(12*x + 17) - 60*(x**3 + 5*x**2 - 2*x - 2)*sin(12*x + 17) with respect to x from 1 to 3.", "answer": "320*cos(53) - 10*cos(29)", "expr": "5*(3*x**2 + 10*x - 2)*cos(12*x + 17) - 60*(x**3 + 5*x**2 - 2*x - 2)*sin(12*x + 17)", "primitive": "5*(x**3 + 5*x**2 - 2*x - 2)*cos(12*x + 17)", "lower": "1", "upper": "3", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(7*x**3 + 5*x**2 - 9*x - 7)/(x**2 + 19)**2 + (21*x**2 + 10*x - 9)/(x**2 + 19) with respect to x from 1 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 257/35", "id": "calculus-L2-8432ddd5dc9615012e6d", "source_id": "calculus-8432ddd5dc9615012e6d", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(7*x**3 + 5*x**2 - 9*x - 7)/(x**2 + 19)**2 + (21*x**2 + 10*x - 9)/(x**2 + 19) with respect to x from 1 to 3.", "answer": "257/35", "expr": "-2*x*(7*x**3 + 5*x**2 - 9*x - 7)/(x**2 + 19)**2 + (21*x**2 + 10*x - 9)/(x**2 + 19)", "primitive": "(7*x**3 + 5*x**2 - 9*x - 7)/(x**2 + 19)", "lower": "1", "upper": "3", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (19*exp(x) + 9)*(-8*x**2 - 2*x - 4) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (-16*x - 2)*(19*exp(x) + 9) + 19*(-8*x**2 - 2*x - 4)*exp(x)", "id": "calculus-L2-1960c214b6df91c0776f", "source_id": "calculus-1960c214b6df91c0776f", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (19*exp(x) + 9)*(-8*x**2 - 2*x - 4) with respect to x.", "answer": "(-16*x - 2)*(19*exp(x) + 9) + 19*(-8*x**2 - 2*x - 4)*exp(x)", "expr": "(19*exp(x) + 9)*(-8*x**2 - 2*x - 4)", "primitive": "(19*exp(x) + 9)*(-8*x**2 - 2*x - 4)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 78*x*exp(3*x**2 + 9) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 13*exp(3*x**2 + 9)", "id": "calculus-L2-d6d3e50b191648f86759", "source_id": "calculus-d6d3e50b191648f86759", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 78*x*exp(3*x**2 + 9) with respect to x.", "answer": "13*exp(3*x**2 + 9)", "expr": "78*x*exp(3*x**2 + 9)", "primitive": "13*exp(3*x**2 + 9)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of 52*x*exp(2*x**2 + 1) with respect to x from 0 to 2. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -13*E + 13*exp(9)", "id": "calculus-L2-09d900332ca9b2f1ba51", "source_id": "calculus-09d900332ca9b2f1ba51", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of 52*x*exp(2*x**2 + 1) with respect to x from 0 to 2.", "answer": "-13*E + 13*exp(9)", "expr": "52*x*exp(2*x**2 + 1)", "primitive": "13*exp(2*x**2 + 1)", "lower": "0", "upper": "2", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (3*x**3 + 3*x**2 + 6*x + 9)/(x**2 + 13) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(3*x**3 + 3*x**2 + 6*x + 9)/(x**2 + 13)**2 + (9*x**2 + 6*x + 6)/(x**2 + 13)", "id": "calculus-L2-a227489fe28718e7521b", "source_id": "calculus-a227489fe28718e7521b", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (3*x**3 + 3*x**2 + 6*x + 9)/(x**2 + 13) with respect to x.", "answer": "-2*x*(3*x**3 + 3*x**2 + 6*x + 9)/(x**2 + 13)**2 + (9*x**2 + 6*x + 6)/(x**2 + 13)", "expr": "(3*x**3 + 3*x**2 + 6*x + 9)/(x**2 + 13)", "primitive": "(3*x**3 + 3*x**2 + 6*x + 9)/(x**2 + 13)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of 14*(3 - 14*x)*log(12*x + 13) + 168*(-7*x**2 + 3*x + 4)/(12*x + 13) with respect to x from 1 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -700*log(49)", "id": "calculus-L2-e66d23a04acddbf76763", "source_id": "calculus-e66d23a04acddbf76763", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of 14*(3 - 14*x)*log(12*x + 13) + 168*(-7*x**2 + 3*x + 4)/(12*x + 13) with respect to x from 1 to 3.", "answer": "-700*log(49)", "expr": "14*(3 - 14*x)*log(12*x + 13) + 168*(-7*x**2 + 3*x + 4)/(12*x + 13)", "primitive": "14*(-7*x**2 + 3*x + 4)*log(12*x + 13)", "lower": "1", "upper": "3", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(-7*x**3 - 4*x**2 + 8*x)/(x**2 + 10)**2 + (-21*x**2 - 8*x + 8)/(x**2 + 10) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (-7*x**3 - 4*x**2 + 8*x)/(x**2 + 10)", "id": "calculus-L2-3003feeba776ae6272b1", "source_id": "calculus-3003feeba776ae6272b1", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(-7*x**3 - 4*x**2 + 8*x)/(x**2 + 10)**2 + (-21*x**2 - 8*x + 8)/(x**2 + 10) with respect to x.", "answer": "(-7*x**3 - 4*x**2 + 8*x)/(x**2 + 10)", "expr": "-2*x*(-7*x**3 - 4*x**2 + 8*x)/(x**2 + 10)**2 + (-21*x**2 - 8*x + 8)/(x**2 + 10)", "primitive": "(-7*x**3 - 4*x**2 + 8*x)/(x**2 + 10)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 2*(-6*x**3 - 5*x**2 + 7)*log(10*x + 6) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 2*(-18*x**2 - 10*x)*log(10*x + 6) + 20*(-6*x**3 - 5*x**2 + 7)/(10*x + 6)", "id": "calculus-L2-b0826a1359e7fb4af848", "source_id": "calculus-b0826a1359e7fb4af848", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 2*(-6*x**3 - 5*x**2 + 7)*log(10*x + 6) with respect to x.", "answer": "2*(-18*x**2 - 10*x)*log(10*x + 6) + 20*(-6*x**3 - 5*x**2 + 7)/(10*x + 6)", "expr": "2*(-6*x**3 - 5*x**2 + 7)*log(10*x + 6)", "primitive": "2*(-6*x**3 - 5*x**2 + 7)*log(10*x + 6)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -6*sin(6*x)*sin(9*x) + 9*cos(6*x)*cos(9*x) with respect to x from 0 to 1. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: sin(9)*cos(6)", "id": "calculus-L2-8868b3f2d7535b1f083c", "source_id": "calculus-8868b3f2d7535b1f083c", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -6*sin(6*x)*sin(9*x) + 9*cos(6*x)*cos(9*x) with respect to x from 0 to 1.", "answer": "sin(9)*cos(6)", "expr": "-6*sin(6*x)*sin(9*x) + 9*cos(6*x)*cos(9*x)", "primitive": "sin(9*x)*cos(6*x)", "lower": "0", "upper": "1", "split": "dev"}
{"instruction": "Evaluate the definite integral of -11*sin(5*x)*sin(11*x) + 5*cos(5*x)*cos(11*x) with respect to x from 1 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: sin(15)*cos(33) - sin(5)*cos(11)", "id": "calculus-L2-ea56a60b8ab6e2011463", "source_id": "calculus-ea56a60b8ab6e2011463", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -11*sin(5*x)*sin(11*x) + 5*cos(5*x)*cos(11*x) with respect to x from 1 to 3.", "answer": "sin(15)*cos(33) - sin(5)*cos(11)", "expr": "-11*sin(5*x)*sin(11*x) + 5*cos(5*x)*cos(11*x)", "primitive": "sin(5*x)*cos(11*x)", "lower": "1", "upper": "3", "split": "dev"}
{"instruction": "Evaluate the definite integral of 5*(-12*x**3 - 18*x**2 - 18*x - 2)*cos(2*x + 15) - 10*(-3*x**4 - 6*x**3 - 9*x**2 - 2*x)*sin(2*x + 15) with respect to x from 2 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 680*cos(19) - 2460*cos(21)", "id": "calculus-L2-736055f51fd05f14b427", "source_id": "calculus-736055f51fd05f14b427", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of 5*(-12*x**3 - 18*x**2 - 18*x - 2)*cos(2*x + 15) - 10*(-3*x**4 - 6*x**3 - 9*x**2 - 2*x)*sin(2*x + 15) with respect to x from 2 to 3.", "answer": "680*cos(19) - 2460*cos(21)", "expr": "5*(-12*x**3 - 18*x**2 - 18*x - 2)*cos(2*x + 15) - 10*(-3*x**4 - 6*x**3 - 9*x**2 - 2*x)*sin(2*x + 15)", "primitive": "5*(-3*x**4 - 6*x**3 - 9*x**2 - 2*x)*cos(2*x + 15)", "lower": "2", "upper": "3", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (4*x**3 - 5*x**2 + x - 2)/(x**2 + 7) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(4*x**3 - 5*x**2 + x - 2)/(x**2 + 7)**2 + (12*x**2 - 10*x + 1)/(x**2 + 7)", "id": "calculus-L2-3aa5eae0a9259ede7218", "source_id": "calculus-3aa5eae0a9259ede7218", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (4*x**3 - 5*x**2 + x - 2)/(x**2 + 7) with respect to x.", "answer": "-2*x*(4*x**3 - 5*x**2 + x - 2)/(x**2 + 7)**2 + (12*x**2 - 10*x + 1)/(x**2 + 7)", "expr": "(4*x**3 - 5*x**2 + x - 2)/(x**2 + 7)", "primitive": "(4*x**3 - 5*x**2 + x - 2)/(x**2 + 7)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 180*log(10*x + 25)*sin(11*x + 30) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 1980*log(10*x + 25)*cos(11*x + 30) + 1800*sin(11*x + 30)/(10*x + 25)", "id": "calculus-L2-52c4e1633532e92a35fc", "source_id": "calculus-52c4e1633532e92a35fc", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 180*log(10*x + 25)*sin(11*x + 30) with respect to x.", "answer": "1980*log(10*x + 25)*cos(11*x + 30) + 1800*sin(11*x + 30)/(10*x + 25)", "expr": "180*log(10*x + 25)*sin(11*x + 30)", "primitive": "180*log(10*x + 25)*sin(11*x + 30)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(4*x**2 + 2*x - 3)/(x**2 + 14)**2 + (8*x + 2)/(x**2 + 14) with respect to x from 2 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 311/414", "id": "calculus-L2-e923fcc6910fba19e65b", "source_id": "calculus-e923fcc6910fba19e65b", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(4*x**2 + 2*x - 3)/(x**2 + 14)**2 + (8*x + 2)/(x**2 + 14) with respect to x from 2 to 3.", "answer": "311/414", "expr": "-2*x*(4*x**2 + 2*x - 3)/(x**2 + 14)**2 + (8*x + 2)/(x**2 + 14)", "primitive": "(4*x**2 + 2*x - 3)/(x**2 + 14)", "lower": "2", "upper": "3", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(x - 2)/(x**2 + 12)**2 + 1/(x**2 + 12) with respect to x from 0 to 1. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 7/78", "id": "calculus-L2-b5075cd4b7be1562af59", "source_id": "calculus-b5075cd4b7be1562af59", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(x - 2)/(x**2 + 12)**2 + 1/(x**2 + 12) with respect to x from 0 to 1.", "answer": "7/78", "expr": "-2*x*(x - 2)/(x**2 + 12)**2 + 1/(x**2 + 12)", "primitive": "(x - 2)/(x**2 + 12)", "lower": "0", "upper": "1", "split": "dev"}
{"instruction": "Find the derivative of f(x) = sin(8*x)*cos(15*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -15*sin(8*x)*sin(15*x) + 8*cos(8*x)*cos(15*x)", "id": "calculus-L2-201bc62bc6bb9b15172a", "source_id": "calculus-201bc62bc6bb9b15172a", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = sin(8*x)*cos(15*x) with respect to x.", "answer": "-15*sin(8*x)*sin(15*x) + 8*cos(8*x)*cos(15*x)", "expr": "sin(8*x)*cos(15*x)", "primitive": "sin(8*x)*cos(15*x)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 4*(7*exp(11*x) + 11)*sin(x + 28) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 4*(7*exp(11*x) + 11)*cos(x + 28) + 308*exp(11*x)*sin(x + 28)", "id": "calculus-L2-2247ab4ffdcbf507116d", "source_id": "calculus-2247ab4ffdcbf507116d", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 4*(7*exp(11*x) + 11)*sin(x + 28) with respect to x.", "answer": "4*(7*exp(11*x) + 11)*cos(x + 28) + 308*exp(11*x)*sin(x + 28)", "expr": "4*(7*exp(11*x) + 11)*sin(x + 28)", "primitive": "4*(7*exp(11*x) + 11)*sin(x + 28)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 10*x*exp(5*x**2 + 20) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: exp(5*x**2 + 20)", "id": "calculus-L2-0c5f6f825f33aa048e20", "source_id": "calculus-0c5f6f825f33aa048e20", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 10*x*exp(5*x**2 + 20) with respect to x.", "answer": "exp(5*x**2 + 20)", "expr": "10*x*exp(5*x**2 + 20)", "primitive": "exp(5*x**2 + 20)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -36*(15*exp(9*x) + 26)*sin(9*x + 29) + 540*exp(9*x)*cos(9*x + 29) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 4*(15*exp(9*x) + 26)*cos(9*x + 29)", "id": "calculus-L2-12c96636a0f4acdd85b3", "source_id": "calculus-12c96636a0f4acdd85b3", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -36*(15*exp(9*x) + 26)*sin(9*x + 29) + 540*exp(9*x)*cos(9*x + 29) with respect to x.", "answer": "4*(15*exp(9*x) + 26)*cos(9*x + 29)", "expr": "-36*(15*exp(9*x) + 26)*sin(9*x + 29) + 540*exp(9*x)*cos(9*x + 29)", "primitive": "4*(15*exp(9*x) + 26)*cos(9*x + 29)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 8*exp(3*x**2 + 17) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 48*x*exp(3*x**2 + 17)", "id": "calculus-L2-d6303821506729d5a1b4", "source_id": "calculus-d6303821506729d5a1b4", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 8*exp(3*x**2 + 17) with respect to x.", "answer": "48*x*exp(3*x**2 + 17)", "expr": "8*exp(3*x**2 + 17)", "primitive": "8*exp(3*x**2 + 17)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -810*log(x + 21)*sin(x + 25) + 810*cos(x + 25)/(x + 21) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 810*log(x + 21)*cos(x + 25)", "id": "calculus-L2-37e249d59c9df87c35cc", "source_id": "calculus-37e249d59c9df87c35cc", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -810*log(x + 21)*sin(x + 25) + 810*cos(x + 25)/(x + 21) with respect to x.", "answer": "810*log(x + 21)*cos(x + 25)", "expr": "-810*log(x + 21)*sin(x + 25) + 810*cos(x + 25)/(x + 21)", "primitive": "810*log(x + 21)*cos(x + 25)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 16*(32*x**3 + 3*x**2 + 4*x - 5)*sin(3*x + 19) + 48*(8*x**4 + x**3 + 2*x**2 - 5*x - 2)*cos(3*x + 19) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 16*(8*x**4 + x**3 + 2*x**2 - 5*x - 2)*sin(3*x + 19)", "id": "calculus-L2-06281582db694b490e45", "source_id": "calculus-06281582db694b490e45", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 16*(32*x**3 + 3*x**2 + 4*x - 5)*sin(3*x + 19) + 48*(8*x**4 + x**3 + 2*x**2 - 5*x - 2)*cos(3*x + 19) with respect to x.", "answer": "16*(8*x**4 + x**3 + 2*x**2 - 5*x - 2)*sin(3*x + 19)", "expr": "16*(32*x**3 + 3*x**2 + 4*x - 5)*sin(3*x + 19) + 48*(8*x**4 + x**3 + 2*x**2 - 5*x - 2)*cos(3*x + 19)", "primitive": "16*(8*x**4 + x**3 + 2*x**2 - 5*x - 2)*sin(3*x + 19)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(2*x + 2)/(x**2 + 9)**2 + 2/(x**2 + 9) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (2*x + 2)/(x**2 + 9)", "id": "calculus-L2-d6c8119a392c5709e095", "source_id": "calculus-d6c8119a392c5709e095", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(2*x + 2)/(x**2 + 9)**2 + 2/(x**2 + 9) with respect to x.", "answer": "(2*x + 2)/(x**2 + 9)", "expr": "-2*x*(2*x + 2)/(x**2 + 9)**2 + 2/(x**2 + 9)", "primitive": "(2*x + 2)/(x**2 + 9)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 2*exp(5*x**2 + 11) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 20*x*exp(5*x**2 + 11)", "id": "calculus-L2-ef5e79c8081760e7f3ab", "source_id": "calculus-ef5e79c8081760e7f3ab", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 2*exp(5*x**2 + 11) with respect to x.", "answer": "20*x*exp(5*x**2 + 11)", "expr": "2*exp(5*x**2 + 11)", "primitive": "2*exp(5*x**2 + 11)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 18*exp(7*x**2 + 14) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 252*x*exp(7*x**2 + 14)", "id": "calculus-L2-18d41c5ecd33e436f0dc", "source_id": "calculus-18d41c5ecd33e436f0dc", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 18*exp(7*x**2 + 14) with respect to x.", "answer": "252*x*exp(7*x**2 + 14)", "expr": "18*exp(7*x**2 + 14)", "primitive": "18*exp(7*x**2 + 14)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -312*(20*exp(10*x) + 25)*sin(12*x + 15) + 5200*exp(10*x)*cos(12*x + 15) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 26*(20*exp(10*x) + 25)*cos(12*x + 15)", "id": "calculus-L2-0e964ff9af63816b835e", "source_id": "calculus-0e964ff9af63816b835e", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -312*(20*exp(10*x) + 25)*sin(12*x + 15) + 5200*exp(10*x)*cos(12*x + 15) with respect to x.", "answer": "26*(20*exp(10*x) + 25)*cos(12*x + 15)", "expr": "-312*(20*exp(10*x) + 25)*sin(12*x + 15) + 5200*exp(10*x)*cos(12*x + 15)", "primitive": "26*(20*exp(10*x) + 25)*cos(12*x + 15)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 9*exp(3*x**2 + 18) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 54*x*exp(3*x**2 + 18)", "id": "calculus-L2-aa3b17b050cb66114aa8", "source_id": "calculus-aa3b17b050cb66114aa8", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 9*exp(3*x**2 + 18) with respect to x.", "answer": "54*x*exp(3*x**2 + 18)", "expr": "9*exp(3*x**2 + 18)", "primitive": "9*exp(3*x**2 + 18)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 8*(-7*x**2 - 3*x - 1)*log(6*x + 23) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 8*(-14*x - 3)*log(6*x + 23) + 48*(-7*x**2 - 3*x - 1)/(6*x + 23)", "id": "calculus-L2-8f46bf4234421de509bb", "source_id": "calculus-8f46bf4234421de509bb", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 8*(-7*x**2 - 3*x - 1)*log(6*x + 23) with respect to x.", "answer": "8*(-14*x - 3)*log(6*x + 23) + 48*(-7*x**2 - 3*x - 1)/(6*x + 23)", "expr": "8*(-7*x**2 - 3*x - 1)*log(6*x + 23)", "primitive": "8*(-7*x**2 - 3*x - 1)*log(6*x + 23)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (3*x**2 + 9*x - 8)/(x**2 + 7) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(3*x**2 + 9*x - 8)/(x**2 + 7)**2 + (6*x + 9)/(x**2 + 7)", "id": "calculus-L2-e7ba9c837ee192224687", "source_id": "calculus-e7ba9c837ee192224687", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (3*x**2 + 9*x - 8)/(x**2 + 7) with respect to x.", "answer": "-2*x*(3*x**2 + 9*x - 8)/(x**2 + 7)**2 + (6*x + 9)/(x**2 + 7)", "expr": "(3*x**2 + 9*x - 8)/(x**2 + 7)", "primitive": "(3*x**2 + 9*x - 8)/(x**2 + 7)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(-x**3 + 9*x**2 - 3*x + 2)/(x**2 + 11)**2 + (-3*x**2 + 18*x - 3)/(x**2 + 11) with respect to x from 1 to 2. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 61/60", "id": "calculus-L2-c9b328fad155af23886d", "source_id": "calculus-c9b328fad155af23886d", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(-x**3 + 9*x**2 - 3*x + 2)/(x**2 + 11)**2 + (-3*x**2 + 18*x - 3)/(x**2 + 11) with respect to x from 1 to 2.", "answer": "61/60", "expr": "-2*x*(-x**3 + 9*x**2 - 3*x + 2)/(x**2 + 11)**2 + (-3*x**2 + 18*x - 3)/(x**2 + 11)", "primitive": "(-x**3 + 9*x**2 - 3*x + 2)/(x**2 + 11)", "lower": "1", "upper": "2", "split": "dev"}
{"instruction": "Evaluate the definite integral of 19*(-16*x**3 + 24*x**2 + 8*x - 8)*sin(8*x + 7) + 152*(-4*x**4 + 8*x**3 + 4*x**2 - 8*x - 3)*cos(8*x + 7) with respect to x from 0 to 1. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -57*sin(15) + 57*sin(7)", "id": "calculus-L2-2efe11454a12e523423e", "source_id": "calculus-2efe11454a12e523423e", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of 19*(-16*x**3 + 24*x**2 + 8*x - 8)*sin(8*x + 7) + 152*(-4*x**4 + 8*x**3 + 4*x**2 - 8*x - 3)*cos(8*x + 7) with respect to x from 0 to 1.", "answer": "-57*sin(15) + 57*sin(7)", "expr": "19*(-16*x**3 + 24*x**2 + 8*x - 8)*sin(8*x + 7) + 152*(-4*x**4 + 8*x**3 + 4*x**2 - 8*x - 3)*cos(8*x + 7)", "primitive": "19*(-4*x**4 + 8*x**3 + 4*x**2 - 8*x - 3)*sin(8*x + 7)", "lower": "0", "upper": "1", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(-9*x**3 + 9*x**2 + 4)/(x**2 + 13)**2 + (-27*x**2 + 18*x)/(x**2 + 13) with respect to x from 1 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -575/77", "id": "calculus-L2-9cb5d68019279a426949", "source_id": "calculus-9cb5d68019279a426949", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(-9*x**3 + 9*x**2 + 4)/(x**2 + 13)**2 + (-27*x**2 + 18*x)/(x**2 + 13) with respect to x from 1 to 3.", "answer": "-575/77", "expr": "-2*x*(-9*x**3 + 9*x**2 + 4)/(x**2 + 13)**2 + (-27*x**2 + 18*x)/(x**2 + 13)", "primitive": "(-9*x**3 + 9*x**2 + 4)/(x**2 + 13)", "lower": "1", "upper": "3", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (-9*x**2 + 7*x + 1)/(x**2 + 20) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(-9*x**2 + 7*x + 1)/(x**2 + 20)**2 + (7 - 18*x)/(x**2 + 20)", "id": "calculus-L2-4ae2841fa2a40468e8c6", "source_id": "calculus-4ae2841fa2a40468e8c6", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (-9*x**2 + 7*x + 1)/(x**2 + 20) with respect to x.", "answer": "-2*x*(-9*x**2 + 7*x + 1)/(x**2 + 20)**2 + (7 - 18*x)/(x**2 + 20)", "expr": "(-9*x**2 + 7*x + 1)/(x**2 + 20)", "primitive": "(-9*x**2 + 7*x + 1)/(x**2 + 20)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(6*x**3 - 7*x**2 - 3*x + 2)/(x**2 + 14)**2 + (18*x**2 - 14*x - 3)/(x**2 + 14) with respect to x from 1 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 62/15", "id": "calculus-L2-1f2790faf3dd91a4059d", "source_id": "calculus-1f2790faf3dd91a4059d", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(6*x**3 - 7*x**2 - 3*x + 2)/(x**2 + 14)**2 + (18*x**2 - 14*x - 3)/(x**2 + 14) with respect to x from 1 to 3.", "answer": "62/15", "expr": "-2*x*(6*x**3 - 7*x**2 - 3*x + 2)/(x**2 + 14)**2 + (18*x**2 - 14*x - 3)/(x**2 + 14)", "primitive": "(6*x**3 - 7*x**2 - 3*x + 2)/(x**2 + 14)", "lower": "1", "upper": "3", "split": "dev"}
{"instruction": "Find an antiderivative of 104*x*exp(4*x**2 + 12) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 13*exp(4*x**2 + 12)", "id": "calculus-L2-af931bebcc5837be67a4", "source_id": "calculus-af931bebcc5837be67a4", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 104*x*exp(4*x**2 + 12) with respect to x.", "answer": "13*exp(4*x**2 + 12)", "expr": "104*x*exp(4*x**2 + 12)", "primitive": "13*exp(4*x**2 + 12)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (-2*x**3 - x**2 + x + 7)/(x**2 + 16) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(-2*x**3 - x**2 + x + 7)/(x**2 + 16)**2 + (-6*x**2 - 2*x + 1)/(x**2 + 16)", "id": "calculus-L2-952753b567193c0c0d44", "source_id": "calculus-952753b567193c0c0d44", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (-2*x**3 - x**2 + x + 7)/(x**2 + 16) with respect to x.", "answer": "-2*x*(-2*x**3 - x**2 + x + 7)/(x**2 + 16)**2 + (-6*x**2 - 2*x + 1)/(x**2 + 16)", "expr": "(-2*x**3 - x**2 + x + 7)/(x**2 + 16)", "primitive": "(-2*x**3 - x**2 + x + 7)/(x**2 + 16)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 36*x*exp(3*x**2 + 19) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 6*exp(3*x**2 + 19)", "id": "calculus-L2-b7f725fd869db40b9849", "source_id": "calculus-b7f725fd869db40b9849", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 36*x*exp(3*x**2 + 19) with respect to x.", "answer": "6*exp(3*x**2 + 19)", "expr": "36*x*exp(3*x**2 + 19)", "primitive": "6*exp(3*x**2 + 19)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2001*sin(3*x + 12)*cos(6*x + 13) - 4002*sin(6*x + 13)*cos(3*x + 12) with respect to x from 2 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -667*cos(18)*cos(25) + 667*cos(21)*cos(31)", "id": "calculus-L2-c3b669eae2c245bb25ba", "source_id": "calculus-c3b669eae2c245bb25ba", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2001*sin(3*x + 12)*cos(6*x + 13) - 4002*sin(6*x + 13)*cos(3*x + 12) with respect to x from 2 to 3.", "answer": "-667*cos(18)*cos(25) + 667*cos(21)*cos(31)", "expr": "-2001*sin(3*x + 12)*cos(6*x + 13) - 4002*sin(6*x + 13)*cos(3*x + 12)", "primitive": "667*cos(3*x + 12)*cos(6*x + 13)", "lower": "2", "upper": "3", "split": "dev"}
{"instruction": "Evaluate the definite integral of -1764*sin(7*x + 7)*cos(8*x + 17) - 2016*sin(8*x + 17)*cos(7*x + 7) with respect to x from 0 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -252*cos(7)*cos(17) + 252*cos(28)*cos(41)", "id": "calculus-L2-bba3de59758d3c9074d9", "source_id": "calculus-bba3de59758d3c9074d9", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -1764*sin(7*x + 7)*cos(8*x + 17) - 2016*sin(8*x + 17)*cos(7*x + 7) with respect to x from 0 to 3.", "answer": "-252*cos(7)*cos(17) + 252*cos(28)*cos(41)", "expr": "-1764*sin(7*x + 7)*cos(8*x + 17) - 2016*sin(8*x + 17)*cos(7*x + 7)", "primitive": "252*cos(7*x + 7)*cos(8*x + 17)", "lower": "0", "upper": "3", "split": "dev"}
{"instruction": "Find an antiderivative of -12*(10*exp(3*x) + 7)*sin(3*x + 27) + 120*exp(3*x)*cos(3*x + 27) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 4*(10*exp(3*x) + 7)*cos(3*x + 27)", "id": "calculus-L2-fe6399050ce96681fd0f", "source_id": "calculus-fe6399050ce96681fd0f", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -12*(10*exp(3*x) + 7)*sin(3*x + 27) + 120*exp(3*x)*cos(3*x + 27) with respect to x.", "answer": "4*(10*exp(3*x) + 7)*cos(3*x + 27)", "expr": "-12*(10*exp(3*x) + 7)*sin(3*x + 27) + 120*exp(3*x)*cos(3*x + 27)", "primitive": "4*(10*exp(3*x) + 7)*cos(3*x + 27)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of 15*(18*x**2 - 10*x + 5)*log(6*x + 29) + 90*(6*x**3 - 5*x**2 + 5*x - 4)/(6*x + 29) with respect to x from 0 to 1. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 30*log(35) + 60*log(29)", "id": "calculus-L2-d894242391c08ff4d499", "source_id": "calculus-d894242391c08ff4d499", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of 15*(18*x**2 - 10*x + 5)*log(6*x + 29) + 90*(6*x**3 - 5*x**2 + 5*x - 4)/(6*x + 29) with respect to x from 0 to 1.", "answer": "30*log(35) + 60*log(29)", "expr": "15*(18*x**2 - 10*x + 5)*log(6*x + 29) + 90*(6*x**3 - 5*x**2 + 5*x - 4)/(6*x + 29)", "primitive": "15*(6*x**3 - 5*x**2 + 5*x - 4)*log(6*x + 29)", "lower": "0", "upper": "1", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(5*x**2 + 5*x - 3)/(x**2 + 10)**2 + (10*x + 5)/(x**2 + 10) with respect to x from 1 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 26/11", "id": "calculus-L2-fe1d8d832dabb85cf72a", "source_id": "calculus-fe1d8d832dabb85cf72a", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(5*x**2 + 5*x - 3)/(x**2 + 10)**2 + (10*x + 5)/(x**2 + 10) with respect to x from 1 to 3.", "answer": "26/11", "expr": "-2*x*(5*x**2 + 5*x - 3)/(x**2 + 10)**2 + (10*x + 5)/(x**2 + 10)", "primitive": "(5*x**2 + 5*x - 3)/(x**2 + 10)", "lower": "1", "upper": "3", "split": "dev"}
{"instruction": "Find an antiderivative of -968*sin(5*x + 27)*sin(11*x + 9) + 440*cos(5*x + 27)*cos(11*x + 9) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 88*sin(5*x + 27)*cos(11*x + 9)", "id": "calculus-L2-260fc8d6e296a9e30874", "source_id": "calculus-260fc8d6e296a9e30874", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -968*sin(5*x + 27)*sin(11*x + 9) + 440*cos(5*x + 27)*cos(11*x + 9) with respect to x.", "answer": "88*sin(5*x + 27)*cos(11*x + 9)", "expr": "-968*sin(5*x + 27)*sin(11*x + 9) + 440*cos(5*x + 27)*cos(11*x + 9)", "primitive": "88*sin(5*x + 27)*cos(11*x + 9)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (8*x**3 - 7*x**2 - 6*x - 6)/(x**2 + 7) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(8*x**3 - 7*x**2 - 6*x - 6)/(x**2 + 7)**2 + (24*x**2 - 14*x - 6)/(x**2 + 7)", "id": "calculus-L2-cdeb04a42821108d3390", "source_id": "calculus-cdeb04a42821108d3390", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (8*x**3 - 7*x**2 - 6*x - 6)/(x**2 + 7) with respect to x.", "answer": "-2*x*(8*x**3 - 7*x**2 - 6*x - 6)/(x**2 + 7)**2 + (24*x**2 - 14*x - 6)/(x**2 + 7)", "expr": "(8*x**3 - 7*x**2 - 6*x - 6)/(x**2 + 7)", "primitive": "(8*x**3 - 7*x**2 - 6*x - 6)/(x**2 + 7)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of (8 - 16*x)*(11*exp(10*x) + 3) + 110*(-8*x**2 + 8*x - 5)*exp(10*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (11*exp(10*x) + 3)*(-8*x**2 + 8*x - 5)", "id": "calculus-L2-b83e45a524ef3ea2949a", "source_id": "calculus-b83e45a524ef3ea2949a", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of (8 - 16*x)*(11*exp(10*x) + 3) + 110*(-8*x**2 + 8*x - 5)*exp(10*x) with respect to x.", "answer": "(11*exp(10*x) + 3)*(-8*x**2 + 8*x - 5)", "expr": "(8 - 16*x)*(11*exp(10*x) + 3) + 110*(-8*x**2 + 8*x - 5)*exp(10*x)", "primitive": "(11*exp(10*x) + 3)*(-8*x**2 + 8*x - 5)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(4*x - 1)/(x**2 + 20)**2 + 4/(x**2 + 20) with respect to x from 1 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 48/203", "id": "calculus-L2-bf70d07b56ebcd656621", "source_id": "calculus-bf70d07b56ebcd656621", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(4*x - 1)/(x**2 + 20)**2 + 4/(x**2 + 20) with respect to x from 1 to 3.", "answer": "48/203", "expr": "-2*x*(4*x - 1)/(x**2 + 20)**2 + 4/(x**2 + 20)", "primitive": "(4*x - 1)/(x**2 + 20)", "lower": "1", "upper": "3", "split": "dev"}
{"instruction": "Evaluate the definite integral of -15*sin(5*x)*sin(15*x) + 5*cos(5*x)*cos(15*x) with respect to x from 0 to 2. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: sin(10)*cos(30)", "id": "calculus-L2-d26e00789eea17e0e4d4", "source_id": "calculus-d26e00789eea17e0e4d4", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -15*sin(5*x)*sin(15*x) + 5*cos(5*x)*cos(15*x) with respect to x from 0 to 2.", "answer": "sin(10)*cos(30)", "expr": "-15*sin(5*x)*sin(15*x) + 5*cos(5*x)*cos(15*x)", "primitive": "sin(5*x)*cos(15*x)", "lower": "0", "upper": "2", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(-9*x**2 - 9*x + 6)/(x**2 + 15)**2 + (-18*x - 9)/(x**2 + 15) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (-9*x**2 - 9*x + 6)/(x**2 + 15)", "id": "calculus-L2-069ae19bccd3304dd054", "source_id": "calculus-069ae19bccd3304dd054", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(-9*x**2 - 9*x + 6)/(x**2 + 15)**2 + (-18*x - 9)/(x**2 + 15) with respect to x.", "answer": "(-9*x**2 - 9*x + 6)/(x**2 + 15)", "expr": "-2*x*(-9*x**2 - 9*x + 6)/(x**2 + 15)**2 + (-18*x - 9)/(x**2 + 15)", "primitive": "(-9*x**2 - 9*x + 6)/(x**2 + 15)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(3*x**3 + 9*x**2 + 6*x - 7)/(x**2 + 12)**2 + (9*x**2 + 18*x + 6)/(x**2 + 12) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (3*x**3 + 9*x**2 + 6*x - 7)/(x**2 + 12)", "id": "calculus-L2-2152a82981341a45f19c", "source_id": "calculus-2152a82981341a45f19c", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(3*x**3 + 9*x**2 + 6*x - 7)/(x**2 + 12)**2 + (9*x**2 + 18*x + 6)/(x**2 + 12) with respect to x.", "answer": "(3*x**3 + 9*x**2 + 6*x - 7)/(x**2 + 12)", "expr": "-2*x*(3*x**3 + 9*x**2 + 6*x - 7)/(x**2 + 12)**2 + (9*x**2 + 18*x + 6)/(x**2 + 12)", "primitive": "(3*x**3 + 9*x**2 + 6*x - 7)/(x**2 + 12)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 8*x*exp(x**2 + 7) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 4*exp(x**2 + 7)", "id": "calculus-L2-44b7b5818fab687103d7", "source_id": "calculus-44b7b5818fab687103d7", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 8*x*exp(x**2 + 7) with respect to x.", "answer": "4*exp(x**2 + 7)", "expr": "8*x*exp(x**2 + 7)", "primitive": "4*exp(x**2 + 7)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 266*x*exp(7*x**2 + 2) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 19*exp(7*x**2 + 2)", "id": "calculus-L2-7caf3e69b3ef4a136f8f", "source_id": "calculus-7caf3e69b3ef4a136f8f", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 266*x*exp(7*x**2 + 2) with respect to x.", "answer": "19*exp(7*x**2 + 2)", "expr": "266*x*exp(7*x**2 + 2)", "primitive": "19*exp(7*x**2 + 2)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(-5*x**2 + x - 2)/(x**2 + 4)**2 + (1 - 10*x)/(x**2 + 4) with respect to x from 0 to 2. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2", "id": "calculus-L2-f2ac688507db6cdd0135", "source_id": "calculus-f2ac688507db6cdd0135", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(-5*x**2 + x - 2)/(x**2 + 4)**2 + (1 - 10*x)/(x**2 + 4) with respect to x from 0 to 2.", "answer": "-2", "expr": "-2*x*(-5*x**2 + x - 2)/(x**2 + 4)**2 + (1 - 10*x)/(x**2 + 4)", "primitive": "(-5*x**2 + x - 2)/(x**2 + 4)", "lower": "0", "upper": "2", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 7*exp(9*x**2 + 15) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 126*x*exp(9*x**2 + 15)", "id": "calculus-L2-5e439c2dee8c3418ced8", "source_id": "calculus-5e439c2dee8c3418ced8", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 7*exp(9*x**2 + 15) with respect to x.", "answer": "126*x*exp(9*x**2 + 15)", "expr": "7*exp(9*x**2 + 15)", "primitive": "7*exp(9*x**2 + 15)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 13*(26*exp(7*x) + 15)*log(8*x + 17) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 2366*exp(7*x)*log(8*x + 17) + 104*(26*exp(7*x) + 15)/(8*x + 17)", "id": "calculus-L2-6292e704c268a9e9dd46", "source_id": "calculus-6292e704c268a9e9dd46", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 13*(26*exp(7*x) + 15)*log(8*x + 17) with respect to x.", "answer": "2366*exp(7*x)*log(8*x + 17) + 104*(26*exp(7*x) + 15)/(8*x + 17)", "expr": "13*(26*exp(7*x) + 15)*log(8*x + 17)", "primitive": "13*(26*exp(7*x) + 15)*log(8*x + 17)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 308*log(3*x + 17)*sin(10*x + 27) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 3080*log(3*x + 17)*cos(10*x + 27) + 924*sin(10*x + 27)/(3*x + 17)", "id": "calculus-L2-2cba24fe8afd5904cc8c", "source_id": "calculus-2cba24fe8afd5904cc8c", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 308*log(3*x + 17)*sin(10*x + 27) with respect to x.", "answer": "3080*log(3*x + 17)*cos(10*x + 27) + 924*sin(10*x + 27)/(3*x + 17)", "expr": "308*log(3*x + 17)*sin(10*x + 27)", "primitive": "308*log(3*x + 17)*sin(10*x + 27)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (9*x**2 - 4*x + 9)/(x**2 + 9) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(9*x**2 - 4*x + 9)/(x**2 + 9)**2 + (18*x - 4)/(x**2 + 9)", "id": "calculus-L2-5156c3298ae3f0de1983", "source_id": "calculus-5156c3298ae3f0de1983", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (9*x**2 - 4*x + 9)/(x**2 + 9) with respect to x.", "answer": "-2*x*(9*x**2 - 4*x + 9)/(x**2 + 9)**2 + (18*x - 4)/(x**2 + 9)", "expr": "(9*x**2 - 4*x + 9)/(x**2 + 9)", "primitive": "(9*x**2 - 4*x + 9)/(x**2 + 9)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -624*log(x + 19)*sin(4*x + 21) + 156*cos(4*x + 21)/(x + 19) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 156*log(x + 19)*cos(4*x + 21)", "id": "calculus-L2-93101000ff69ebad58a0", "source_id": "calculus-93101000ff69ebad58a0", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -624*log(x + 19)*sin(4*x + 21) + 156*cos(4*x + 21)/(x + 19) with respect to x.", "answer": "156*log(x + 19)*cos(4*x + 21)", "expr": "-624*log(x + 19)*sin(4*x + 21) + 156*cos(4*x + 21)/(x + 19)", "primitive": "156*log(x + 19)*cos(4*x + 21)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 20*exp(9*x**2 + 5) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 360*x*exp(9*x**2 + 5)", "id": "calculus-L2-d223a3e7b85e990b4126", "source_id": "calculus-d223a3e7b85e990b4126", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 20*exp(9*x**2 + 5) with respect to x.", "answer": "360*x*exp(9*x**2 + 5)", "expr": "20*exp(9*x**2 + 5)", "primitive": "20*exp(9*x**2 + 5)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (9*x + 1)/(x**2 + 14) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(9*x + 1)/(x**2 + 14)**2 + 9/(x**2 + 14)", "id": "calculus-L2-8f5110dbba124f2fa80f", "source_id": "calculus-8f5110dbba124f2fa80f", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (9*x + 1)/(x**2 + 14) with respect to x.", "answer": "-2*x*(9*x + 1)/(x**2 + 14)**2 + 9/(x**2 + 14)", "expr": "(9*x + 1)/(x**2 + 14)", "primitive": "(9*x + 1)/(x**2 + 14)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -144*(25*exp(12*x) + 20)*sin(8*x + 6) + 5400*exp(12*x)*cos(8*x + 6) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 18*(25*exp(12*x) + 20)*cos(8*x + 6)", "id": "calculus-L2-e5f996c476fc4990042f", "source_id": "calculus-e5f996c476fc4990042f", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -144*(25*exp(12*x) + 20)*sin(8*x + 6) + 5400*exp(12*x)*cos(8*x + 6) with respect to x.", "answer": "18*(25*exp(12*x) + 20)*cos(8*x + 6)", "expr": "-144*(25*exp(12*x) + 20)*sin(8*x + 6) + 5400*exp(12*x)*cos(8*x + 6)", "primitive": "18*(25*exp(12*x) + 20)*cos(8*x + 6)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (2*x - 9)/(x**2 + 4) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(2*x - 9)/(x**2 + 4)**2 + 2/(x**2 + 4)", "id": "calculus-L2-ac4678e5b9619fad7f7f", "source_id": "calculus-ac4678e5b9619fad7f7f", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (2*x - 9)/(x**2 + 4) with respect to x.", "answer": "-2*x*(2*x - 9)/(x**2 + 4)**2 + 2/(x**2 + 4)", "expr": "(2*x - 9)/(x**2 + 4)", "primitive": "(2*x - 9)/(x**2 + 4)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 19*exp(9*x**2 + 5) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 342*x*exp(9*x**2 + 5)", "id": "calculus-L2-52f3894755fb254adeaa", "source_id": "calculus-52f3894755fb254adeaa", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 19*exp(9*x**2 + 5) with respect to x.", "answer": "342*x*exp(9*x**2 + 5)", "expr": "19*exp(9*x**2 + 5)", "primitive": "19*exp(9*x**2 + 5)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 14*x**2/(x**2 + 1)**2 - 7/(x**2 + 1) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -7*x/(x**2 + 1)", "id": "calculus-L2-3df2029978525a3095ea", "source_id": "calculus-3df2029978525a3095ea", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 14*x**2/(x**2 + 1)**2 - 7/(x**2 + 1) with respect to x.", "answer": "-7*x/(x**2 + 1)", "expr": "14*x**2/(x**2 + 1)**2 - 7/(x**2 + 1)", "primitive": "-7*x/(x**2 + 1)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(-3*x**2 + 3*x + 7)/(x**2 + 9)**2 + (3 - 6*x)/(x**2 + 9) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (-3*x**2 + 3*x + 7)/(x**2 + 9)", "id": "calculus-L2-a370a0847e8b1cc49306", "source_id": "calculus-a370a0847e8b1cc49306", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(-3*x**2 + 3*x + 7)/(x**2 + 9)**2 + (3 - 6*x)/(x**2 + 9) with respect to x.", "answer": "(-3*x**2 + 3*x + 7)/(x**2 + 9)", "expr": "-2*x*(-3*x**2 + 3*x + 7)/(x**2 + 9)**2 + (3 - 6*x)/(x**2 + 9)", "primitive": "(-3*x**2 + 3*x + 7)/(x**2 + 9)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(4*x**3 - 7*x**2 - x + 8)/(x**2 + 5)**2 + (12*x**2 - 14*x - 1)/(x**2 + 5) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (4*x**3 - 7*x**2 - x + 8)/(x**2 + 5)", "id": "calculus-L2-134d43e89c72f67d0d37", "source_id": "calculus-134d43e89c72f67d0d37", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(4*x**3 - 7*x**2 - x + 8)/(x**2 + 5)**2 + (12*x**2 - 14*x - 1)/(x**2 + 5) with respect to x.", "answer": "(4*x**3 - 7*x**2 - x + 8)/(x**2 + 5)", "expr": "-2*x*(4*x**3 - 7*x**2 - x + 8)/(x**2 + 5)**2 + (12*x**2 - 14*x - 1)/(x**2 + 5)", "primitive": "(4*x**3 - 7*x**2 - x + 8)/(x**2 + 5)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (-9*x**2 + 2*x - 8)/(x**2 + 16) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(-9*x**2 + 2*x - 8)/(x**2 + 16)**2 + (2 - 18*x)/(x**2 + 16)", "id": "calculus-L2-6341fafa842e9def278d", "source_id": "calculus-6341fafa842e9def278d", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (-9*x**2 + 2*x - 8)/(x**2 + 16) with respect to x.", "answer": "-2*x*(-9*x**2 + 2*x - 8)/(x**2 + 16)**2 + (2 - 18*x)/(x**2 + 16)", "expr": "(-9*x**2 + 2*x - 8)/(x**2 + 16)", "primitive": "(-9*x**2 + 2*x - 8)/(x**2 + 16)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 16*exp(7*x**2 + 6) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 224*x*exp(7*x**2 + 6)", "id": "calculus-L2-5042803d595e6f0fa847", "source_id": "calculus-5042803d595e6f0fa847", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 16*exp(7*x**2 + 6) with respect to x.", "answer": "224*x*exp(7*x**2 + 6)", "expr": "16*exp(7*x**2 + 6)", "primitive": "16*exp(7*x**2 + 6)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 7*exp(5*x**2 + 6) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 70*x*exp(5*x**2 + 6)", "id": "calculus-L2-dc32fe877523d0931b00", "source_id": "calculus-dc32fe877523d0931b00", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 7*exp(5*x**2 + 6) with respect to x.", "answer": "70*x*exp(5*x**2 + 6)", "expr": "7*exp(5*x**2 + 6)", "primitive": "7*exp(5*x**2 + 6)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 3800*log(9*x + 3)*cos(8*x + 17) + 4275*sin(8*x + 17)/(9*x + 3) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 475*log(9*x + 3)*sin(8*x + 17)", "id": "calculus-L2-09947ee23c37f73eaa15", "source_id": "calculus-09947ee23c37f73eaa15", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 3800*log(9*x + 3)*cos(8*x + 17) + 4275*sin(8*x + 17)/(9*x + 3) with respect to x.", "answer": "475*log(9*x + 3)*sin(8*x + 17)", "expr": "3800*log(9*x + 3)*cos(8*x + 17) + 4275*sin(8*x + 17)/(9*x + 3)", "primitive": "475*log(9*x + 3)*sin(8*x + 17)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -12*sin(4*x)*sin(12*x) + 4*cos(4*x)*cos(12*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: sin(4*x)*cos(12*x)", "id": "calculus-L2-3469e29e993f3a4a6c0d", "source_id": "calculus-3469e29e993f3a4a6c0d", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -12*sin(4*x)*sin(12*x) + 4*cos(4*x)*cos(12*x) with respect to x.", "answer": "sin(4*x)*cos(12*x)", "expr": "-12*sin(4*x)*sin(12*x) + 4*cos(4*x)*cos(12*x)", "primitive": "sin(4*x)*cos(12*x)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -18*sin(7*x)*sin(18*x) + 7*cos(7*x)*cos(18*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: sin(7*x)*cos(18*x)", "id": "calculus-L2-37654d23af62ca18c82d", "source_id": "calculus-37654d23af62ca18c82d", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -18*sin(7*x)*sin(18*x) + 7*cos(7*x)*cos(18*x) with respect to x.", "answer": "sin(7*x)*cos(18*x)", "expr": "-18*sin(7*x)*sin(18*x) + 7*cos(7*x)*cos(18*x)", "primitive": "sin(7*x)*cos(18*x)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(3 - 9*x)/(x**2 + 6)**2 - 9/(x**2 + 6) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (3 - 9*x)/(x**2 + 6)", "id": "calculus-L2-7181b272ef4ff8bc561a", "source_id": "calculus-7181b272ef4ff8bc561a", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(3 - 9*x)/(x**2 + 6)**2 - 9/(x**2 + 6) with respect to x.", "answer": "(3 - 9*x)/(x**2 + 6)", "expr": "-2*x*(3 - 9*x)/(x**2 + 6)**2 - 9/(x**2 + 6)", "primitive": "(3 - 9*x)/(x**2 + 6)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 15*(36*x**3 - 24*x**2 + 14*x + 2)*log(9*x + 13) + 135*(9*x**4 - 8*x**3 + 7*x**2 + 2*x - 1)/(9*x + 13) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 15*(9*x**4 - 8*x**3 + 7*x**2 + 2*x - 1)*log(9*x + 13)", "id": "calculus-L2-c4337d3747a87f271f49", "source_id": "calculus-c4337d3747a87f271f49", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 15*(36*x**3 - 24*x**2 + 14*x + 2)*log(9*x + 13) + 135*(9*x**4 - 8*x**3 + 7*x**2 + 2*x - 1)/(9*x + 13) with respect to x.", "answer": "15*(9*x**4 - 8*x**3 + 7*x**2 + 2*x - 1)*log(9*x + 13)", "expr": "15*(36*x**3 - 24*x**2 + 14*x + 2)*log(9*x + 13) + 135*(9*x**4 - 8*x**3 + 7*x**2 + 2*x - 1)/(9*x + 13)", "primitive": "15*(9*x**4 - 8*x**3 + 7*x**2 + 2*x - 1)*log(9*x + 13)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(9*x**2 - 9*x + 6)/(x**2 + 9)**2 + (18*x - 9)/(x**2 + 9) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (9*x**2 - 9*x + 6)/(x**2 + 9)", "id": "calculus-L2-103561b6a4e367e619a2", "source_id": "calculus-103561b6a4e367e619a2", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(9*x**2 - 9*x + 6)/(x**2 + 9)**2 + (18*x - 9)/(x**2 + 9) with respect to x.", "answer": "(9*x**2 - 9*x + 6)/(x**2 + 9)", "expr": "-2*x*(9*x**2 - 9*x + 6)/(x**2 + 9)**2 + (18*x - 9)/(x**2 + 9)", "primitive": "(9*x**2 - 9*x + 6)/(x**2 + 9)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 18*exp(7*x**2 + 12) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 252*x*exp(7*x**2 + 12)", "id": "calculus-L2-30acc288c66d1496cdb7", "source_id": "calculus-30acc288c66d1496cdb7", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 18*exp(7*x**2 + 12) with respect to x.", "answer": "252*x*exp(7*x**2 + 12)", "expr": "18*exp(7*x**2 + 12)", "primitive": "18*exp(7*x**2 + 12)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 272*x*exp(8*x**2 + 7) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 17*exp(8*x**2 + 7)", "id": "calculus-L2-f4c0207b4d45a227e443", "source_id": "calculus-f4c0207b4d45a227e443", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 272*x*exp(8*x**2 + 7) with respect to x.", "answer": "17*exp(8*x**2 + 7)", "expr": "272*x*exp(8*x**2 + 7)", "primitive": "17*exp(8*x**2 + 7)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 198*log(10*x + 13)*cos(9*x + 13) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -1782*log(10*x + 13)*sin(9*x + 13) + 1980*cos(9*x + 13)/(10*x + 13)", "id": "calculus-L2-76ca19efb911004c51eb", "source_id": "calculus-76ca19efb911004c51eb", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 198*log(10*x + 13)*cos(9*x + 13) with respect to x.", "answer": "-1782*log(10*x + 13)*sin(9*x + 13) + 1980*cos(9*x + 13)/(10*x + 13)", "expr": "198*log(10*x + 13)*cos(9*x + 13)", "primitive": "198*log(10*x + 13)*cos(9*x + 13)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of (8*x + 6)*(2*x**3 - x**2 - 9*x - 8) + (4*x**2 + 6*x - 1)*(6*x**2 - 2*x - 9) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (4*x**2 + 6*x - 1)*(2*x**3 - x**2 - 9*x - 8)", "id": "calculus-L2-e66d4172626001914d70", "source_id": "calculus-e66d4172626001914d70", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of (8*x + 6)*(2*x**3 - x**2 - 9*x - 8) + (4*x**2 + 6*x - 1)*(6*x**2 - 2*x - 9) with respect to x.", "answer": "(4*x**2 + 6*x - 1)*(2*x**3 - x**2 - 9*x - 8)", "expr": "(8*x + 6)*(2*x**3 - x**2 - 9*x - 8) + (4*x**2 + 6*x - 1)*(6*x**2 - 2*x - 9)", "primitive": "(4*x**2 + 6*x - 1)*(2*x**3 - x**2 - 9*x - 8)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(2*x**2 - 3*x + 2)/(x**2 + 6)**2 + (4*x - 3)/(x**2 + 6) with respect to x from 1 to 2. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 9/35", "id": "calculus-L2-b0fa415b46a289b84c09", "source_id": "calculus-b0fa415b46a289b84c09", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(2*x**2 - 3*x + 2)/(x**2 + 6)**2 + (4*x - 3)/(x**2 + 6) with respect to x from 1 to 2.", "answer": "9/35", "expr": "-2*x*(2*x**2 - 3*x + 2)/(x**2 + 6)**2 + (4*x - 3)/(x**2 + 6)", "primitive": "(2*x**2 - 3*x + 2)/(x**2 + 6)", "lower": "1", "upper": "2", "split": "dev"}
{"instruction": "Find an antiderivative of (24*x**2 - 5)*(4*x**4 - 5*x**3 - 7*x**2 - 2*x - 3) + (8*x**3 - 5*x - 2)*(16*x**3 - 15*x**2 - 14*x - 2) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (8*x**3 - 5*x - 2)*(4*x**4 - 5*x**3 - 7*x**2 - 2*x - 3)", "id": "calculus-L2-75dcdd3081b45470f368", "source_id": "calculus-75dcdd3081b45470f368", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of (24*x**2 - 5)*(4*x**4 - 5*x**3 - 7*x**2 - 2*x - 3) + (8*x**3 - 5*x - 2)*(16*x**3 - 15*x**2 - 14*x - 2) with respect to x.", "answer": "(8*x**3 - 5*x - 2)*(4*x**4 - 5*x**3 - 7*x**2 - 2*x - 3)", "expr": "(24*x**2 - 5)*(4*x**4 - 5*x**3 - 7*x**2 - 2*x - 3) + (8*x**3 - 5*x - 2)*(16*x**3 - 15*x**2 - 14*x - 2)", "primitive": "(8*x**3 - 5*x - 2)*(4*x**4 - 5*x**3 - 7*x**2 - 2*x - 3)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -980*log(x + 26)*sin(5*x + 13) + 196*cos(5*x + 13)/(x + 26) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 196*log(x + 26)*cos(5*x + 13)", "id": "calculus-L2-16938770f8af4d9ea14d", "source_id": "calculus-16938770f8af4d9ea14d", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -980*log(x + 26)*sin(5*x + 13) + 196*cos(5*x + 13)/(x + 26) with respect to x.", "answer": "196*log(x + 26)*cos(5*x + 13)", "expr": "-980*log(x + 26)*sin(5*x + 13) + 196*cos(5*x + 13)/(x + 26)", "primitive": "196*log(x + 26)*cos(5*x + 13)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 19*(15*x**2 - 10*x - 7)*cos(5*x + 13) - 95*(5*x**3 - 5*x**2 - 7*x + 3)*sin(5*x + 13) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 19*(5*x**3 - 5*x**2 - 7*x + 3)*cos(5*x + 13)", "id": "calculus-L2-64ba8231b46421c7cf28", "source_id": "calculus-64ba8231b46421c7cf28", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 19*(15*x**2 - 10*x - 7)*cos(5*x + 13) - 95*(5*x**3 - 5*x**2 - 7*x + 3)*sin(5*x + 13) with respect to x.", "answer": "19*(5*x**3 - 5*x**2 - 7*x + 3)*cos(5*x + 13)", "expr": "19*(15*x**2 - 10*x - 7)*cos(5*x + 13) - 95*(5*x**3 - 5*x**2 - 7*x + 3)*sin(5*x + 13)", "primitive": "19*(5*x**3 - 5*x**2 - 7*x + 3)*cos(5*x + 13)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of 5148*log(6*x + 30)*cos(9*x + 2) + 3432*sin(9*x + 2)/(6*x + 30) with respect to x from 1 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 572*log(48)*sin(29) - 572*log(36)*sin(11)", "id": "calculus-L2-74df26b89a878001c551", "source_id": "calculus-74df26b89a878001c551", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of 5148*log(6*x + 30)*cos(9*x + 2) + 3432*sin(9*x + 2)/(6*x + 30) with respect to x from 1 to 3.", "answer": "572*log(48)*sin(29) - 572*log(36)*sin(11)", "expr": "5148*log(6*x + 30)*cos(9*x + 2) + 3432*sin(9*x + 2)/(6*x + 30)", "primitive": "572*log(6*x + 30)*sin(9*x + 2)", "lower": "1", "upper": "3", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(-7*x**3 - 9*x**2 + 5*x + 7)/(x**2 + 16)**2 + (-21*x**2 - 18*x + 5)/(x**2 + 16) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (-7*x**3 - 9*x**2 + 5*x + 7)/(x**2 + 16)", "id": "calculus-L2-77f6f60b2e595d7188b4", "source_id": "calculus-77f6f60b2e595d7188b4", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(-7*x**3 - 9*x**2 + 5*x + 7)/(x**2 + 16)**2 + (-21*x**2 - 18*x + 5)/(x**2 + 16) with respect to x.", "answer": "(-7*x**3 - 9*x**2 + 5*x + 7)/(x**2 + 16)", "expr": "-2*x*(-7*x**3 - 9*x**2 + 5*x + 7)/(x**2 + 16)**2 + (-21*x**2 - 18*x + 5)/(x**2 + 16)", "primitive": "(-7*x**3 - 9*x**2 + 5*x + 7)/(x**2 + 16)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (x + 8)/(x**2 + 18) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(x + 8)/(x**2 + 18)**2 + 1/(x**2 + 18)", "id": "calculus-L2-83c0469e9376365b26a9", "source_id": "calculus-83c0469e9376365b26a9", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (x + 8)/(x**2 + 18) with respect to x.", "answer": "-2*x*(x + 8)/(x**2 + 18)**2 + 1/(x**2 + 18)", "expr": "(x + 8)/(x**2 + 18)", "primitive": "(x + 8)/(x**2 + 18)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(-9*x - 7)/(x**2 + 19)**2 - 9/(x**2 + 19) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (-9*x - 7)/(x**2 + 19)", "id": "calculus-L2-7e1f7dfd3a26d61488ad", "source_id": "calculus-7e1f7dfd3a26d61488ad", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(-9*x - 7)/(x**2 + 19)**2 - 9/(x**2 + 19) with respect to x.", "answer": "(-9*x - 7)/(x**2 + 19)", "expr": "-2*x*(-9*x - 7)/(x**2 + 19)**2 - 9/(x**2 + 19)", "primitive": "(-9*x - 7)/(x**2 + 19)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (5*x**3 + 6*x**2 - 7*x + 7)/(x**2 + 20) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(5*x**3 + 6*x**2 - 7*x + 7)/(x**2 + 20)**2 + (15*x**2 + 12*x - 7)/(x**2 + 20)", "id": "calculus-L2-1887e6897322651550af", "source_id": "calculus-1887e6897322651550af", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (5*x**3 + 6*x**2 - 7*x + 7)/(x**2 + 20) with respect to x.", "answer": "-2*x*(5*x**3 + 6*x**2 - 7*x + 7)/(x**2 + 20)**2 + (15*x**2 + 12*x - 7)/(x**2 + 20)", "expr": "(5*x**3 + 6*x**2 - 7*x + 7)/(x**2 + 20)", "primitive": "(5*x**3 + 6*x**2 - 7*x + 7)/(x**2 + 20)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = sin(6*x)*cos(13*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -13*sin(6*x)*sin(13*x) + 6*cos(6*x)*cos(13*x)", "id": "calculus-L2-553716209d391fe35aee", "source_id": "calculus-553716209d391fe35aee", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = sin(6*x)*cos(13*x) with respect to x.", "answer": "-13*sin(6*x)*sin(13*x) + 6*cos(6*x)*cos(13*x)", "expr": "sin(6*x)*cos(13*x)", "primitive": "sin(6*x)*cos(13*x)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 232*(12*exp(9*x) + 20)*cos(8*x + 25) + 3132*exp(9*x)*sin(8*x + 25) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 29*(12*exp(9*x) + 20)*sin(8*x + 25)", "id": "calculus-L2-28f0e2078fa069ae1ae1", "source_id": "calculus-28f0e2078fa069ae1ae1", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 232*(12*exp(9*x) + 20)*cos(8*x + 25) + 3132*exp(9*x)*sin(8*x + 25) with respect to x.", "answer": "29*(12*exp(9*x) + 20)*sin(8*x + 25)", "expr": "232*(12*exp(9*x) + 20)*cos(8*x + 25) + 3132*exp(9*x)*sin(8*x + 25)", "primitive": "29*(12*exp(9*x) + 20)*sin(8*x + 25)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 30*(5*x**4 - 3*x**3 + 6*x**2 + 3*x - 7)*cos(6*x + 28) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 30*(20*x**3 - 9*x**2 + 12*x + 3)*cos(6*x + 28) - 180*(5*x**4 - 3*x**3 + 6*x**2 + 3*x - 7)*sin(6*x + 28)", "id": "calculus-L2-066763ba5cd313c5e3a5", "source_id": "calculus-066763ba5cd313c5e3a5", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 30*(5*x**4 - 3*x**3 + 6*x**2 + 3*x - 7)*cos(6*x + 28) with respect to x.", "answer": "30*(20*x**3 - 9*x**2 + 12*x + 3)*cos(6*x + 28) - 180*(5*x**4 - 3*x**3 + 6*x**2 + 3*x - 7)*sin(6*x + 28)", "expr": "30*(5*x**4 - 3*x**3 + 6*x**2 + 3*x - 7)*cos(6*x + 28)", "primitive": "30*(5*x**4 - 3*x**3 + 6*x**2 + 3*x - 7)*cos(6*x + 28)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -4*sin(4*x)*sin(7*x) + 7*cos(4*x)*cos(7*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: sin(7*x)*cos(4*x)", "id": "calculus-L2-c45c097799d56019bde3", "source_id": "calculus-c45c097799d56019bde3", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -4*sin(4*x)*sin(7*x) + 7*cos(4*x)*cos(7*x) with respect to x.", "answer": "sin(7*x)*cos(4*x)", "expr": "-4*sin(4*x)*sin(7*x) + 7*cos(4*x)*cos(7*x)", "primitive": "sin(7*x)*cos(4*x)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of (-27*x**2 - 1)*(9*exp(11*x) + 9) + 99*(-9*x**3 - x - 3)*exp(11*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (9*exp(11*x) + 9)*(-9*x**3 - x - 3)", "id": "calculus-L2-f7cf2d47d192d532fc62", "source_id": "calculus-f7cf2d47d192d532fc62", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of (-27*x**2 - 1)*(9*exp(11*x) + 9) + 99*(-9*x**3 - x - 3)*exp(11*x) with respect to x.", "answer": "(9*exp(11*x) + 9)*(-9*x**3 - x - 3)", "expr": "(-27*x**2 - 1)*(9*exp(11*x) + 9) + 99*(-9*x**3 - x - 3)*exp(11*x)", "primitive": "(9*exp(11*x) + 9)*(-9*x**3 - x - 3)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 11*exp(7*x**2 + 7) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 154*x*exp(7*x**2 + 7)", "id": "calculus-L2-32404c84230736b8ad6d", "source_id": "calculus-32404c84230736b8ad6d", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 11*exp(7*x**2 + 7) with respect to x.", "answer": "154*x*exp(7*x**2 + 7)", "expr": "11*exp(7*x**2 + 7)", "primitive": "11*exp(7*x**2 + 7)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 11*(-24*x**3 - 9*x**2 + 16*x - 5)*log(x + 18) + 11*(-6*x**4 - 3*x**3 + 8*x**2 - 5*x - 6)/(x + 18) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 11*(-6*x**4 - 3*x**3 + 8*x**2 - 5*x - 6)*log(x + 18)", "id": "calculus-L2-de46ffa1941eb7c803f3", "source_id": "calculus-de46ffa1941eb7c803f3", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 11*(-24*x**3 - 9*x**2 + 16*x - 5)*log(x + 18) + 11*(-6*x**4 - 3*x**3 + 8*x**2 - 5*x - 6)/(x + 18) with respect to x.", "answer": "11*(-6*x**4 - 3*x**3 + 8*x**2 - 5*x - 6)*log(x + 18)", "expr": "11*(-24*x**3 - 9*x**2 + 16*x - 5)*log(x + 18) + 11*(-6*x**4 - 3*x**3 + 8*x**2 - 5*x - 6)/(x + 18)", "primitive": "11*(-6*x**4 - 3*x**3 + 8*x**2 - 5*x - 6)*log(x + 18)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (6*x**3 - 3*x**2 - 5*x + 9)/(x**2 + 11) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(6*x**3 - 3*x**2 - 5*x + 9)/(x**2 + 11)**2 + (18*x**2 - 6*x - 5)/(x**2 + 11)", "id": "calculus-L2-58ea9dd1c7de5527eebf", "source_id": "calculus-58ea9dd1c7de5527eebf", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (6*x**3 - 3*x**2 - 5*x + 9)/(x**2 + 11) with respect to x.", "answer": "-2*x*(6*x**3 - 3*x**2 - 5*x + 9)/(x**2 + 11)**2 + (18*x**2 - 6*x - 5)/(x**2 + 11)", "expr": "(6*x**3 - 3*x**2 - 5*x + 9)/(x**2 + 11)", "primitive": "(6*x**3 - 3*x**2 - 5*x + 9)/(x**2 + 11)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (-x - 9)/(x**2 + 5) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(-x - 9)/(x**2 + 5)**2 - 1/(x**2 + 5)", "id": "calculus-L2-d33d7e025f25fc8a36c8", "source_id": "calculus-d33d7e025f25fc8a36c8", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (-x - 9)/(x**2 + 5) with respect to x.", "answer": "-2*x*(-x - 9)/(x**2 + 5)**2 - 1/(x**2 + 5)", "expr": "(-x - 9)/(x**2 + 5)", "primitive": "(-x - 9)/(x**2 + 5)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 13*(15*exp(11*x) + 23)*sin(7*x + 2) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 91*(15*exp(11*x) + 23)*cos(7*x + 2) + 2145*exp(11*x)*sin(7*x + 2)", "id": "calculus-L2-8305df876f4292f64ccb", "source_id": "calculus-8305df876f4292f64ccb", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 13*(15*exp(11*x) + 23)*sin(7*x + 2) with respect to x.", "answer": "91*(15*exp(11*x) + 23)*cos(7*x + 2) + 2145*exp(11*x)*sin(7*x + 2)", "expr": "13*(15*exp(11*x) + 23)*sin(7*x + 2)", "primitive": "13*(15*exp(11*x) + 23)*sin(7*x + 2)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 520*log(3*x + 24)*cos(10*x + 15) + 156*sin(10*x + 15)/(3*x + 24) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 52*log(3*x + 24)*sin(10*x + 15)", "id": "calculus-L2-24b8a7c517b916f8cbd3", "source_id": "calculus-24b8a7c517b916f8cbd3", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 520*log(3*x + 24)*cos(10*x + 15) + 156*sin(10*x + 15)/(3*x + 24) with respect to x.", "answer": "52*log(3*x + 24)*sin(10*x + 15)", "expr": "520*log(3*x + 24)*cos(10*x + 15) + 156*sin(10*x + 15)/(3*x + 24)", "primitive": "52*log(3*x + 24)*sin(10*x + 15)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(3 - 4*x)/(x**2 + 9)**2 - 4/(x**2 + 9) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (3 - 4*x)/(x**2 + 9)", "id": "calculus-L2-4f57eb3bcb1dea24fe9b", "source_id": "calculus-4f57eb3bcb1dea24fe9b", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(3 - 4*x)/(x**2 + 9)**2 - 4/(x**2 + 9) with respect to x.", "answer": "(3 - 4*x)/(x**2 + 9)", "expr": "-2*x*(3 - 4*x)/(x**2 + 9)**2 - 4/(x**2 + 9)", "primitive": "(3 - 4*x)/(x**2 + 9)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 18*exp(8*x**2 + 8) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 288*x*exp(8*x**2 + 8)", "id": "calculus-L2-dc2ddd3f7e2b06018376", "source_id": "calculus-dc2ddd3f7e2b06018376", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 18*exp(8*x**2 + 8) with respect to x.", "answer": "288*x*exp(8*x**2 + 8)", "expr": "18*exp(8*x**2 + 8)", "primitive": "18*exp(8*x**2 + 8)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = sin(6*x)*cos(15*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -15*sin(6*x)*sin(15*x) + 6*cos(6*x)*cos(15*x)", "id": "calculus-L2-41266051282695bd7b56", "source_id": "calculus-41266051282695bd7b56", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = sin(6*x)*cos(15*x) with respect to x.", "answer": "-15*sin(6*x)*sin(15*x) + 6*cos(6*x)*cos(15*x)", "expr": "sin(6*x)*cos(15*x)", "primitive": "sin(6*x)*cos(15*x)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -56*sin(7*x + 25)*sin(10*x + 3) + 80*cos(7*x + 25)*cos(10*x + 3) with respect to x from 0 to 1. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -8*sin(3)*cos(25) + 8*sin(13)*cos(32)", "id": "calculus-L2-580b3affc85f3abffd5e", "source_id": "calculus-580b3affc85f3abffd5e", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -56*sin(7*x + 25)*sin(10*x + 3) + 80*cos(7*x + 25)*cos(10*x + 3) with respect to x from 0 to 1.", "answer": "-8*sin(3)*cos(25) + 8*sin(13)*cos(32)", "expr": "-56*sin(7*x + 25)*sin(10*x + 3) + 80*cos(7*x + 25)*cos(10*x + 3)", "primitive": "8*sin(10*x + 3)*cos(7*x + 25)", "lower": "0", "upper": "1", "split": "dev"}
{"instruction": "Find an antiderivative of 112*x*exp(7*x**2 + 11) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 8*exp(7*x**2 + 11)", "id": "calculus-L2-190a0f303bb3970d002c", "source_id": "calculus-190a0f303bb3970d002c", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 112*x*exp(7*x**2 + 11) with respect to x.", "answer": "8*exp(7*x**2 + 11)", "expr": "112*x*exp(7*x**2 + 11)", "primitive": "8*exp(7*x**2 + 11)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 16*x*exp(4*x**2 + 1) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 2*exp(4*x**2 + 1)", "id": "calculus-L2-b34fd4cf1067a194d6db", "source_id": "calculus-b34fd4cf1067a194d6db", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 16*x*exp(4*x**2 + 1) with respect to x.", "answer": "2*exp(4*x**2 + 1)", "expr": "16*x*exp(4*x**2 + 1)", "primitive": "2*exp(4*x**2 + 1)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -4032*sin(12*x + 18)*cos(12*x + 18) with respect to x from 0 to 1. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -168*cos(18)**2 + 168*cos(30)**2", "id": "calculus-L2-70dd5f87e31afeb21572", "source_id": "calculus-70dd5f87e31afeb21572", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -4032*sin(12*x + 18)*cos(12*x + 18) with respect to x from 0 to 1.", "answer": "-168*cos(18)**2 + 168*cos(30)**2", "expr": "-4032*sin(12*x + 18)*cos(12*x + 18)", "primitive": "168*cos(12*x + 18)**2", "lower": "0", "upper": "1", "split": "dev"}
{"instruction": "Evaluate the definite integral of 40*x*exp(x**2 + 4) with respect to x from 0 to 2. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -20*exp(4) + 20*exp(8)", "id": "calculus-L2-596fe4379b7f97f31d1d", "source_id": "calculus-596fe4379b7f97f31d1d", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of 40*x*exp(x**2 + 4) with respect to x from 0 to 2.", "answer": "-20*exp(4) + 20*exp(8)", "expr": "40*x*exp(x**2 + 4)", "primitive": "20*exp(x**2 + 4)", "lower": "0", "upper": "2", "split": "dev"}
{"instruction": "Find an antiderivative of -3519*log(12*x + 29)*sin(9*x + 6) + 4692*cos(9*x + 6)/(12*x + 29) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 391*log(12*x + 29)*cos(9*x + 6)", "id": "calculus-L2-17c20aae37651a98549a", "source_id": "calculus-17c20aae37651a98549a", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -3519*log(12*x + 29)*sin(9*x + 6) + 4692*cos(9*x + 6)/(12*x + 29) with respect to x.", "answer": "391*log(12*x + 29)*cos(9*x + 6)", "expr": "-3519*log(12*x + 29)*sin(9*x + 6) + 4692*cos(9*x + 6)/(12*x + 29)", "primitive": "391*log(12*x + 29)*cos(9*x + 6)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 80*x*exp(2*x**2 + 3) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 20*exp(2*x**2 + 3)", "id": "calculus-L2-f5906e289f8800dcae3d", "source_id": "calculus-f5906e289f8800dcae3d", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 80*x*exp(2*x**2 + 3) with respect to x.", "answer": "20*exp(2*x**2 + 3)", "expr": "80*x*exp(2*x**2 + 3)", "primitive": "20*exp(2*x**2 + 3)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 98*x*exp(7*x**2 + 9) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 7*exp(7*x**2 + 9)", "id": "calculus-L2-a9e4ab9fe3eae85421f2", "source_id": "calculus-a9e4ab9fe3eae85421f2", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 98*x*exp(7*x**2 + 9) with respect to x.", "answer": "7*exp(7*x**2 + 9)", "expr": "98*x*exp(7*x**2 + 9)", "primitive": "7*exp(7*x**2 + 9)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(-x**3 + 2*x**2 - 8*x + 9)/(x**2 + 18)**2 + (-3*x**2 + 4*x - 8)/(x**2 + 18) with respect to x from 1 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -170/171", "id": "calculus-L2-754f91be60c66070316f", "source_id": "calculus-754f91be60c66070316f", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(-x**3 + 2*x**2 - 8*x + 9)/(x**2 + 18)**2 + (-3*x**2 + 4*x - 8)/(x**2 + 18) with respect to x from 1 to 3.", "answer": "-170/171", "expr": "-2*x*(-x**3 + 2*x**2 - 8*x + 9)/(x**2 + 18)**2 + (-3*x**2 + 4*x - 8)/(x**2 + 18)", "primitive": "(-x**3 + 2*x**2 - 8*x + 9)/(x**2 + 18)", "lower": "1", "upper": "3", "split": "dev"}
{"instruction": "Find an antiderivative of 6*x*exp(3*x**2 + 19) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: exp(3*x**2 + 19)", "id": "calculus-L2-86716bae9cc2ed7ecd3d", "source_id": "calculus-86716bae9cc2ed7ecd3d", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 6*x*exp(3*x**2 + 19) with respect to x.", "answer": "exp(3*x**2 + 19)", "expr": "6*x*exp(3*x**2 + 19)", "primitive": "exp(3*x**2 + 19)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 9*exp(x**2 + 12) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 18*x*exp(x**2 + 12)", "id": "calculus-L2-ba0f7637f296769f1a94", "source_id": "calculus-ba0f7637f296769f1a94", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 9*exp(x**2 + 12) with respect to x.", "answer": "18*x*exp(x**2 + 12)", "expr": "9*exp(x**2 + 12)", "primitive": "9*exp(x**2 + 12)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(-7*x**3 + 7*x**2 - 5*x - 4)/(x**2 + 19)**2 + (-21*x**2 + 14*x - 5)/(x**2 + 19) with respect to x from 1 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -331/70", "id": "calculus-L2-00d56b1d045bf634045f", "source_id": "calculus-00d56b1d045bf634045f", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(-7*x**3 + 7*x**2 - 5*x - 4)/(x**2 + 19)**2 + (-21*x**2 + 14*x - 5)/(x**2 + 19) with respect to x from 1 to 3.", "answer": "-331/70", "expr": "-2*x*(-7*x**3 + 7*x**2 - 5*x - 4)/(x**2 + 19)**2 + (-21*x**2 + 14*x - 5)/(x**2 + 19)", "primitive": "(-7*x**3 + 7*x**2 - 5*x - 4)/(x**2 + 19)", "lower": "1", "upper": "3", "split": "dev"}
{"instruction": "Find an antiderivative of 10*x**2/(x**2 + 3)**2 - 5/(x**2 + 3) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -5*x/(x**2 + 3)", "id": "calculus-L2-d6034683f1e5516d9089", "source_id": "calculus-d6034683f1e5516d9089", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 10*x**2/(x**2 + 3)**2 - 5/(x**2 + 3) with respect to x.", "answer": "-5*x/(x**2 + 3)", "expr": "10*x**2/(x**2 + 3)**2 - 5/(x**2 + 3)", "primitive": "-5*x/(x**2 + 3)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(4*x + 6)/(x**2 + 2)**2 + 4/(x**2 + 2) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (4*x + 6)/(x**2 + 2)", "id": "calculus-L2-21affd5d35c0ec0bf2b9", "source_id": "calculus-21affd5d35c0ec0bf2b9", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(4*x + 6)/(x**2 + 2)**2 + 4/(x**2 + 2) with respect to x.", "answer": "(4*x + 6)/(x**2 + 2)", "expr": "-2*x*(4*x + 6)/(x**2 + 2)**2 + 4/(x**2 + 2)", "primitive": "(4*x + 6)/(x**2 + 2)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 84*x*exp(6*x**2 + 3) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 7*exp(6*x**2 + 3)", "id": "calculus-L2-0411ae6698a6966f5e08", "source_id": "calculus-0411ae6698a6966f5e08", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 84*x*exp(6*x**2 + 3) with respect to x.", "answer": "7*exp(6*x**2 + 3)", "expr": "84*x*exp(6*x**2 + 3)", "primitive": "7*exp(6*x**2 + 3)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of (17*exp(6*x) + 24)*(32*x**3 + 21*x**2 + 18*x + 8) + 102*(8*x**4 + 7*x**3 + 9*x**2 + 8*x - 1)*exp(6*x) with respect to x from 0 to 1. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 785 + 527*exp(6)", "id": "calculus-L2-9847bec661756c18b70d", "source_id": "calculus-9847bec661756c18b70d", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of (17*exp(6*x) + 24)*(32*x**3 + 21*x**2 + 18*x + 8) + 102*(8*x**4 + 7*x**3 + 9*x**2 + 8*x - 1)*exp(6*x) with respect to x from 0 to 1.", "answer": "785 + 527*exp(6)", "expr": "(17*exp(6*x) + 24)*(32*x**3 + 21*x**2 + 18*x + 8) + 102*(8*x**4 + 7*x**3 + 9*x**2 + 8*x - 1)*exp(6*x)", "primitive": "(17*exp(6*x) + 24)*(8*x**4 + 7*x**3 + 9*x**2 + 8*x - 1)", "lower": "0", "upper": "1", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(7 - 6*x)/(x**2 + 8)**2 - 6/(x**2 + 8) with respect to x from 0 to 1. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -55/72", "id": "calculus-L2-c353b4586108d2b5ca0b", "source_id": "calculus-c353b4586108d2b5ca0b", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(7 - 6*x)/(x**2 + 8)**2 - 6/(x**2 + 8) with respect to x from 0 to 1.", "answer": "-55/72", "expr": "-2*x*(7 - 6*x)/(x**2 + 8)**2 - 6/(x**2 + 8)", "primitive": "(7 - 6*x)/(x**2 + 8)", "lower": "0", "upper": "1", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (-2*x**3 - 8*x**2 + 5*x + 3)/(x**2 + 18) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(-2*x**3 - 8*x**2 + 5*x + 3)/(x**2 + 18)**2 + (-6*x**2 - 16*x + 5)/(x**2 + 18)", "id": "calculus-L2-6fea5bd79b65405f8232", "source_id": "calculus-6fea5bd79b65405f8232", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (-2*x**3 - 8*x**2 + 5*x + 3)/(x**2 + 18) with respect to x.", "answer": "-2*x*(-2*x**3 - 8*x**2 + 5*x + 3)/(x**2 + 18)**2 + (-6*x**2 - 16*x + 5)/(x**2 + 18)", "expr": "(-2*x**3 - 8*x**2 + 5*x + 3)/(x**2 + 18)", "primitive": "(-2*x**3 - 8*x**2 + 5*x + 3)/(x**2 + 18)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(-4*x - 4)/(x**2 + 10)**2 - 4/(x**2 + 10) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (-4*x - 4)/(x**2 + 10)", "id": "calculus-L2-7263fe3e2d9500a8c8dd", "source_id": "calculus-7263fe3e2d9500a8c8dd", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(-4*x - 4)/(x**2 + 10)**2 - 4/(x**2 + 10) with respect to x.", "answer": "(-4*x - 4)/(x**2 + 10)", "expr": "-2*x*(-4*x - 4)/(x**2 + 10)**2 - 4/(x**2 + 10)", "primitive": "(-4*x - 4)/(x**2 + 10)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of (8*x + 9)*(10*exp(8*x) + 28) + 80*(4*x**2 + 9*x - 4)*exp(8*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (10*exp(8*x) + 28)*(4*x**2 + 9*x - 4)", "id": "calculus-L2-e0d6cb93b0e7dadc4963", "source_id": "calculus-e0d6cb93b0e7dadc4963", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of (8*x + 9)*(10*exp(8*x) + 28) + 80*(4*x**2 + 9*x - 4)*exp(8*x) with respect to x.", "answer": "(10*exp(8*x) + 28)*(4*x**2 + 9*x - 4)", "expr": "(8*x + 9)*(10*exp(8*x) + 28) + 80*(4*x**2 + 9*x - 4)*exp(8*x)", "primitive": "(10*exp(8*x) + 28)*(4*x**2 + 9*x - 4)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 238*log(2*x + 16)*log(2*x + 17) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 476*log(2*x + 16)/(2*x + 17) + 476*log(2*x + 17)/(2*x + 16)", "id": "calculus-L2-07f22e738d499d8a7527", "source_id": "calculus-07f22e738d499d8a7527", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 238*log(2*x + 16)*log(2*x + 17) with respect to x.", "answer": "476*log(2*x + 16)/(2*x + 17) + 476*log(2*x + 17)/(2*x + 16)", "expr": "238*log(2*x + 16)*log(2*x + 17)", "primitive": "238*log(2*x + 16)*log(2*x + 17)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(4 - 9*x)/(x**2 + 19)**2 - 9/(x**2 + 19) with respect to x from 1 to 2. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -33/92", "id": "calculus-L2-47d2043c7d123ac20d17", "source_id": "calculus-47d2043c7d123ac20d17", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(4 - 9*x)/(x**2 + 19)**2 - 9/(x**2 + 19) with respect to x from 1 to 2.", "answer": "-33/92", "expr": "-2*x*(4 - 9*x)/(x**2 + 19)**2 - 9/(x**2 + 19)", "primitive": "(4 - 9*x)/(x**2 + 19)", "lower": "1", "upper": "2", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(-4*x**3 - 5*x**2 - x - 3)/(x**2 + 20)**2 + (-12*x**2 - 10*x - 1)/(x**2 + 20) with respect to x from 1 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2962/609", "id": "calculus-L2-48cf2f36a90de1644482", "source_id": "calculus-48cf2f36a90de1644482", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(-4*x**3 - 5*x**2 - x - 3)/(x**2 + 20)**2 + (-12*x**2 - 10*x - 1)/(x**2 + 20) with respect to x from 1 to 3.", "answer": "-2962/609", "expr": "-2*x*(-4*x**3 - 5*x**2 - x - 3)/(x**2 + 20)**2 + (-12*x**2 - 10*x - 1)/(x**2 + 20)", "primitive": "(-4*x**3 - 5*x**2 - x - 3)/(x**2 + 20)", "lower": "1", "upper": "3", "split": "dev"}
{"instruction": "Evaluate the definite integral of -15*sin(9*x)*sin(15*x) + 9*cos(9*x)*cos(15*x) with respect to x from 0 to 1. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: sin(9)*cos(15)", "id": "calculus-L2-41f2daa3f57cb9aec9d8", "source_id": "calculus-41f2daa3f57cb9aec9d8", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -15*sin(9*x)*sin(15*x) + 9*cos(9*x)*cos(15*x) with respect to x from 0 to 1.", "answer": "sin(9)*cos(15)", "expr": "-15*sin(9*x)*sin(15*x) + 9*cos(9*x)*cos(15*x)", "primitive": "sin(9*x)*cos(15*x)", "lower": "0", "upper": "1", "split": "dev"}
{"instruction": "Find an antiderivative of 144*x*exp(9*x**2 + 19) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 8*exp(9*x**2 + 19)", "id": "calculus-L2-ef8c7109d6c28dfeac3b", "source_id": "calculus-ef8c7109d6c28dfeac3b", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 144*x*exp(9*x**2 + 19) with respect to x.", "answer": "8*exp(9*x**2 + 19)", "expr": "144*x*exp(9*x**2 + 19)", "primitive": "8*exp(9*x**2 + 19)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(-5*x**3 + 6*x**2 + x + 5)/(x**2 + 3)**2 + (-15*x**2 + 12*x + 1)/(x**2 + 3) with respect to x from 1 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -47/6", "id": "calculus-L2-f87cbebac02e8b189d7f", "source_id": "calculus-f87cbebac02e8b189d7f", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(-5*x**3 + 6*x**2 + x + 5)/(x**2 + 3)**2 + (-15*x**2 + 12*x + 1)/(x**2 + 3) with respect to x from 1 to 3.", "answer": "-47/6", "expr": "-2*x*(-5*x**3 + 6*x**2 + x + 5)/(x**2 + 3)**2 + (-15*x**2 + 12*x + 1)/(x**2 + 3)", "primitive": "(-5*x**3 + 6*x**2 + x + 5)/(x**2 + 3)", "lower": "1", "upper": "3", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 10*exp(3*x**2 + 17) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 60*x*exp(3*x**2 + 17)", "id": "calculus-L2-cc6f3eae10daeb731625", "source_id": "calculus-cc6f3eae10daeb731625", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 10*exp(3*x**2 + 17) with respect to x.", "answer": "60*x*exp(3*x**2 + 17)", "expr": "10*exp(3*x**2 + 17)", "primitive": "10*exp(3*x**2 + 17)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = exp(9*x**2 + 3) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 18*x*exp(9*x**2 + 3)", "id": "calculus-L2-9247299b32b7ec58966a", "source_id": "calculus-9247299b32b7ec58966a", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = exp(9*x**2 + 3) with respect to x.", "answer": "18*x*exp(9*x**2 + 3)", "expr": "exp(9*x**2 + 3)", "primitive": "exp(9*x**2 + 3)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = sin(4*x)*cos(5*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -5*sin(4*x)*sin(5*x) + 4*cos(4*x)*cos(5*x)", "id": "calculus-L2-faaac53b8e0fbe01d2aa", "source_id": "calculus-faaac53b8e0fbe01d2aa", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = sin(4*x)*cos(5*x) with respect to x.", "answer": "-5*sin(4*x)*sin(5*x) + 4*cos(4*x)*cos(5*x)", "expr": "sin(4*x)*cos(5*x)", "primitive": "sin(4*x)*cos(5*x)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -20*sin(6*x)*sin(20*x) + 6*cos(6*x)*cos(20*x) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: sin(6*x)*cos(20*x)", "id": "calculus-L2-4249b4faf4e3c40cdd00", "source_id": "calculus-4249b4faf4e3c40cdd00", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -20*sin(6*x)*sin(20*x) + 6*cos(6*x)*cos(20*x) with respect to x.", "answer": "sin(6*x)*cos(20*x)", "expr": "-20*sin(6*x)*sin(20*x) + 6*cos(6*x)*cos(20*x)", "primitive": "sin(6*x)*cos(20*x)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 9*exp(7*x**2 + 12) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 126*x*exp(7*x**2 + 12)", "id": "calculus-L2-5f2d41a7033c55b35b2a", "source_id": "calculus-5f2d41a7033c55b35b2a", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 9*exp(7*x**2 + 12) with respect to x.", "answer": "126*x*exp(7*x**2 + 12)", "expr": "9*exp(7*x**2 + 12)", "primitive": "9*exp(7*x**2 + 12)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 9*exp(7*x**2 + 20) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 126*x*exp(7*x**2 + 20)", "id": "calculus-L2-fa3a82c7f3b979e623e5", "source_id": "calculus-fa3a82c7f3b979e623e5", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 9*exp(7*x**2 + 20) with respect to x.", "answer": "126*x*exp(7*x**2 + 20)", "expr": "9*exp(7*x**2 + 20)", "primitive": "9*exp(7*x**2 + 20)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(-4*x**3 + 8*x**2 - 5*x - 7)/(x**2 + 12)**2 + (-12*x**2 + 16*x - 5)/(x**2 + 12) with respect to x from 0 to 2. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -23/48", "id": "calculus-L2-7452b8067df122a2a51a", "source_id": "calculus-7452b8067df122a2a51a", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(-4*x**3 + 8*x**2 - 5*x - 7)/(x**2 + 12)**2 + (-12*x**2 + 16*x - 5)/(x**2 + 12) with respect to x from 0 to 2.", "answer": "-23/48", "expr": "-2*x*(-4*x**3 + 8*x**2 - 5*x - 7)/(x**2 + 12)**2 + (-12*x**2 + 16*x - 5)/(x**2 + 12)", "primitive": "(-4*x**3 + 8*x**2 - 5*x - 7)/(x**2 + 12)", "lower": "0", "upper": "2", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(2 - 5*x)/(x**2 + 16)**2 - 5/(x**2 + 16) with respect to x from 0 to 1. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -41/136", "id": "calculus-L2-a25163444ec81b582795", "source_id": "calculus-a25163444ec81b582795", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(2 - 5*x)/(x**2 + 16)**2 - 5/(x**2 + 16) with respect to x from 0 to 1.", "answer": "-41/136", "expr": "-2*x*(2 - 5*x)/(x**2 + 16)**2 - 5/(x**2 + 16)", "primitive": "(2 - 5*x)/(x**2 + 16)", "lower": "0", "upper": "1", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(2*x + 3)/(x**2 + 17)**2 + 2/(x**2 + 17) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (2*x + 3)/(x**2 + 17)", "id": "calculus-L2-76e000ee81420e8fcf3c", "source_id": "calculus-76e000ee81420e8fcf3c", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(2*x + 3)/(x**2 + 17)**2 + 2/(x**2 + 17) with respect to x.", "answer": "(2*x + 3)/(x**2 + 17)", "expr": "-2*x*(2*x + 3)/(x**2 + 17)**2 + 2/(x**2 + 17)", "primitive": "(2*x + 3)/(x**2 + 17)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (7*x**2 - 9*x + 1)/(x**2 + 2) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(7*x**2 - 9*x + 1)/(x**2 + 2)**2 + (14*x - 9)/(x**2 + 2)", "id": "calculus-L2-1072ffed3b8a09e241be", "source_id": "calculus-1072ffed3b8a09e241be", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (7*x**2 - 9*x + 1)/(x**2 + 2) with respect to x.", "answer": "-2*x*(7*x**2 - 9*x + 1)/(x**2 + 2)**2 + (14*x - 9)/(x**2 + 2)", "expr": "(7*x**2 - 9*x + 1)/(x**2 + 2)", "primitive": "(7*x**2 - 9*x + 1)/(x**2 + 2)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(2*x + 3)/(x**2 + 1)**2 + 2/(x**2 + 1) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (2*x + 3)/(x**2 + 1)", "id": "calculus-L2-777fcbc673a92ae9bca9", "source_id": "calculus-777fcbc673a92ae9bca9", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(2*x + 3)/(x**2 + 1)**2 + 2/(x**2 + 1) with respect to x.", "answer": "(2*x + 3)/(x**2 + 1)", "expr": "-2*x*(2*x + 3)/(x**2 + 1)**2 + 2/(x**2 + 1)", "primitive": "(2*x + 3)/(x**2 + 1)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 10*exp(5*x**2 + 2) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 100*x*exp(5*x**2 + 2)", "id": "calculus-L2-5758d5473774099e8709", "source_id": "calculus-5758d5473774099e8709", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 10*exp(5*x**2 + 2) with respect to x.", "answer": "100*x*exp(5*x**2 + 2)", "expr": "10*exp(5*x**2 + 2)", "primitive": "10*exp(5*x**2 + 2)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -6*sin(4*x)*sin(6*x) + 4*cos(4*x)*cos(6*x) with respect to x from 1 to 2. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -sin(4)*cos(6) + sin(8)*cos(12)", "id": "calculus-L2-1299d2a032137f2677ee", "source_id": "calculus-1299d2a032137f2677ee", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -6*sin(4*x)*sin(6*x) + 4*cos(4*x)*cos(6*x) with respect to x from 1 to 2.", "answer": "-sin(4)*cos(6) + sin(8)*cos(12)", "expr": "-6*sin(4*x)*sin(6*x) + 4*cos(4*x)*cos(6*x)", "primitive": "sin(4*x)*cos(6*x)", "lower": "1", "upper": "2", "split": "dev"}
{"instruction": "Find an antiderivative of 102*x*exp(3*x**2 + 11) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 17*exp(3*x**2 + 11)", "id": "calculus-L2-17dcdc97ded9e0b0586a", "source_id": "calculus-17dcdc97ded9e0b0586a", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 102*x*exp(3*x**2 + 11) with respect to x.", "answer": "17*exp(3*x**2 + 11)", "expr": "102*x*exp(3*x**2 + 11)", "primitive": "17*exp(3*x**2 + 11)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(9*x**3 - 7*x**2)/(x**2 + 17)**2 + (27*x**2 - 14*x)/(x**2 + 17) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (9*x**3 - 7*x**2)/(x**2 + 17)", "id": "calculus-L2-cedda76920ff4ce0ef4d", "source_id": "calculus-cedda76920ff4ce0ef4d", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(9*x**3 - 7*x**2)/(x**2 + 17)**2 + (27*x**2 - 14*x)/(x**2 + 17) with respect to x.", "answer": "(9*x**3 - 7*x**2)/(x**2 + 17)", "expr": "-2*x*(9*x**3 - 7*x**2)/(x**2 + 17)**2 + (27*x**2 - 14*x)/(x**2 + 17)", "primitive": "(9*x**3 - 7*x**2)/(x**2 + 17)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Evaluate the definite integral of -2*x*(5*x**3 - 5*x**2 - 4*x + 9)/(x**2 + 13)**2 + (15*x**2 - 10*x - 4)/(x**2 + 13) with respect to x from 0 to 3. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 933/286", "id": "calculus-L2-b19350fd3358fec2ef14", "source_id": "calculus-b19350fd3358fec2ef14", "topic": "calculus", "level": 2, "kind": "defint", "question": "Evaluate the definite integral of -2*x*(5*x**3 - 5*x**2 - 4*x + 9)/(x**2 + 13)**2 + (15*x**2 - 10*x - 4)/(x**2 + 13) with respect to x from 0 to 3.", "answer": "933/286", "expr": "-2*x*(5*x**3 - 5*x**2 - 4*x + 9)/(x**2 + 13)**2 + (15*x**2 - 10*x - 4)/(x**2 + 13)", "primitive": "(5*x**3 - 5*x**2 - 4*x + 9)/(x**2 + 13)", "lower": "0", "upper": "3", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 17*exp(x**2 + 9) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 34*x*exp(x**2 + 9)", "id": "calculus-L2-78710ad85c13bfb1444f", "source_id": "calculus-78710ad85c13bfb1444f", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 17*exp(x**2 + 9) with respect to x.", "answer": "34*x*exp(x**2 + 9)", "expr": "17*exp(x**2 + 9)", "primitive": "17*exp(x**2 + 9)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of -2*x*(8*x**3 - x**2 + 2*x + 5)/(x**2 + 4)**2 + (24*x**2 - 2*x + 2)/(x**2 + 4) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: (8*x**3 - x**2 + 2*x + 5)/(x**2 + 4)", "id": "calculus-L2-db8c6b5f124f40ddbf6d", "source_id": "calculus-db8c6b5f124f40ddbf6d", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of -2*x*(8*x**3 - x**2 + 2*x + 5)/(x**2 + 4)**2 + (24*x**2 - 2*x + 2)/(x**2 + 4) with respect to x.", "answer": "(8*x**3 - x**2 + 2*x + 5)/(x**2 + 4)", "expr": "-2*x*(8*x**3 - x**2 + 2*x + 5)/(x**2 + 4)**2 + (24*x**2 - 2*x + 2)/(x**2 + 4)", "primitive": "(8*x**3 - x**2 + 2*x + 5)/(x**2 + 4)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find an antiderivative of 6*(28*x**3 - 24*x**2 + 14*x - 2)*log(4*x + 22) + 24*(7*x**4 - 8*x**3 + 7*x**2 - 2*x - 2)/(4*x + 22) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 6*(7*x**4 - 8*x**3 + 7*x**2 - 2*x - 2)*log(4*x + 22)", "id": "calculus-L2-d46842352ab8147ae547", "source_id": "calculus-d46842352ab8147ae547", "topic": "calculus", "level": 2, "kind": "integral", "question": "Find an antiderivative of 6*(28*x**3 - 24*x**2 + 14*x - 2)*log(4*x + 22) + 24*(7*x**4 - 8*x**3 + 7*x**2 - 2*x - 2)/(4*x + 22) with respect to x.", "answer": "6*(7*x**4 - 8*x**3 + 7*x**2 - 2*x - 2)*log(4*x + 22)", "expr": "6*(28*x**3 - 24*x**2 + 14*x - 2)*log(4*x + 22) + 24*(7*x**4 - 8*x**3 + 7*x**2 - 2*x - 2)/(4*x + 22)", "primitive": "6*(7*x**4 - 8*x**3 + 7*x**2 - 2*x - 2)*log(4*x + 22)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 4*(-3*x**2 - 8*x - 6)*sin(6*x + 26) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 4*(-6*x - 8)*sin(6*x + 26) + 24*(-3*x**2 - 8*x - 6)*cos(6*x + 26)", "id": "calculus-L2-6de0cfe921cc94c9b2c9", "source_id": "calculus-6de0cfe921cc94c9b2c9", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 4*(-3*x**2 - 8*x - 6)*sin(6*x + 26) with respect to x.", "answer": "4*(-6*x - 8)*sin(6*x + 26) + 24*(-3*x**2 - 8*x - 6)*cos(6*x + 26)", "expr": "4*(-3*x**2 - 8*x - 6)*sin(6*x + 26)", "primitive": "4*(-3*x**2 - 8*x - 6)*sin(6*x + 26)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = 30*(30*exp(x) + 20)*log(5*x + 3) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: 900*exp(x)*log(5*x + 3) + 150*(30*exp(x) + 20)/(5*x + 3)", "id": "calculus-L2-3af72dfba6be2fe690cd", "source_id": "calculus-3af72dfba6be2fe690cd", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = 30*(30*exp(x) + 20)*log(5*x + 3) with respect to x.", "answer": "900*exp(x)*log(5*x + 3) + 150*(30*exp(x) + 20)/(5*x + 3)", "expr": "30*(30*exp(x) + 20)*log(5*x + 3)", "primitive": "30*(30*exp(x) + 20)*log(5*x + 3)", "lower": "", "upper": "", "split": "dev"}
{"instruction": "Find the derivative of f(x) = (-5*x - 6)/(x**2 + 14) with respect to x. Give the final answer on the last line as 'Answer: <expression>'.", "output": "Answer: -2*x*(-5*x - 6)/(x**2 + 14)**2 - 5/(x**2 + 14)", "id": "calculus-L2-378232fd08ba9badab1f", "source_id": "calculus-378232fd08ba9badab1f", "topic": "calculus", "level": 2, "kind": "diff", "question": "Find the derivative of f(x) = (-5*x - 6)/(x**2 + 14) with respect to x.", "answer": "-2*x*(-5*x - 6)/(x**2 + 14)**2 - 5/(x**2 + 14)", "expr": "(-5*x - 6)/(x**2 + 14)", "primitive": "(-5*x - 6)/(x**2 + 14)", "lower": "", "upper": "", "split": "dev"}