task_id stringlengths 23 52 | subset stringclasses 1
value | family stringclasses 80
values | problem_key stringclasses 75
values | domain stringclasses 8
values | tier stringclasses 2
values | level stringclasses 6
values | source stringclasses 80
values | license stringclasses 3
values | tags listlengths 0 4 | prompt stringlengths 308 37k | instance stringlengths 56 37.8k | direction null | baseline null | best_known null | reference_answer stringlengths 8 198k | reference_reward float64 1 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
construct-rg-intermediate-integration-l6-s6 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 6 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 3*x**5*cos(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin,... | {"variable": "x", "integrand": "3*x**5*cos(x)", "problem_type": "repeated_parts", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "3*x**5*sin(x) + 15*x**4*cos(x) - 60*x**3*sin(x) - 180*x**2*cos(x) + 360*x*sin(x) + 360*cos(x) + C"} | 1 |
construct-rg-intermediate-integration-l6-s7 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 6 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -3*x**5*exp(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin... | {"variable": "x", "integrand": "-3*x**5*exp(x)", "problem_type": "repeated_parts", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "(-3*x**5 + 15*x**4 - 60*x**3 + 180*x**2 - 360*x + 360)*exp(x) + C"} | 1 |
construct-rg-intermediate-integration-l6-s8 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 6 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -x**4*cos(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, ... | {"variable": "x", "integrand": "-x**4*cos(x)", "problem_type": "repeated_parts", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-x**4*sin(x) - 4*x**3*cos(x) + 12*x**2*sin(x) + 24*x*cos(x) - 24*sin(x) + C"} | 1 |
construct-rg-intermediate-integration-l6-s9 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 6 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -3*x**4*exp(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin... | {"variable": "x", "integrand": "-3*x**4*exp(x)", "problem_type": "repeated_parts", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "(-3*x**4 + 12*x**3 - 36*x**2 + 72*x - 72)*exp(x) + C"} | 1 |
construct-rg-simple-integration-l1-s0 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 1 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 9*x/4 + 7/9
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, a... | {"variable": "x", "integrand": "9*x/4 + 7/9", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "9*x**2/8 + 7*x/9 + C"} | 1 |
construct-rg-simple-integration-l1-s1 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 1 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 92*x**3/5
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, aco... | {"variable": "x", "integrand": "92*x**3/5", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "23*x**4/5 + C"} | 1 |
construct-rg-simple-integration-l1-s2 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 1 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 3*x**2/2 - 20*x
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asi... | {"variable": "x", "integrand": "3*x**2/2 - 20*x", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "x**3/2 - 10*x**2 + C"} | 1 |
construct-rg-simple-integration-l1-s3 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 1 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = 5*X**3/2 + 1
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, ... | {"variable": "X", "integrand": "5*X**3/2 + 1", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "5*X**4/8 + X + C"} | 1 |
construct-rg-simple-integration-l1-s4 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 1 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -30*x
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, acos, a... | {"variable": "x", "integrand": "-30*x", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-15*x**2 + C"} | 1 |
construct-rg-simple-integration-l1-s5 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 1 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -27*x**2
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, acos... | {"variable": "x", "integrand": "-27*x**2", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-9*x**3 + C"} | 1 |
construct-rg-simple-integration-l1-s6 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 1 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = -16*X**3 - 6*X
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin... | {"variable": "X", "integrand": "-16*X**3 - 6*X", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-4*X**4 - 3*X**2 + C"} | 1 |
construct-rg-simple-integration-l1-s7 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 1 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 2*x - 5/6
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, aco... | {"variable": "x", "integrand": "2*x - 5/6", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "x**2 - 5*x/6 + C"} | 1 |
construct-rg-simple-integration-l1-s8 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 1 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = 14*X**3/3 + 14*X
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, as... | {"variable": "X", "integrand": "14*X**3/3 + 14*X", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "7*X**4/6 + 7*X**2 + C"} | 1 |
construct-rg-simple-integration-l1-s9 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 1 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 65*x**2/2
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, aco... | {"variable": "x", "integrand": "65*x**2/2", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "65*x**3/6 + C"} | 1 |
construct-rg-simple-integration-l2-s0 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 2 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 7*x**4 - 3*x**2
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asi... | {"variable": "x", "integrand": "7*x**4 - 3*x**2", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "7*x**5/5 - x**3 + C"} | 1 |
construct-rg-simple-integration-l2-s1 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 2 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 3 - 196*x**3/9
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin... | {"variable": "x", "integrand": "3 - 196*x**3/9", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-49*x**4/9 + 3*x + C"} | 1 |
construct-rg-simple-integration-l2-s2 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 2 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 48*x**5 - 20*x - 7/2
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan... | {"variable": "x", "integrand": "48*x**5 - 20*x - 7/2", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "8*x**6 - 10*x**2 - 7*x/2 + C"} | 1 |
construct-rg-simple-integration-l2-s3 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 2 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = 6*X**5 - 5*X**2/3 - 10
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, t... | {"variable": "X", "integrand": "6*X**5 - 5*X**2/3 - 10", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "X**6 - 5*X**3/9 - 10*X + C"} | 1 |
construct-rg-simple-integration-l2-s4 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 2 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = -60*X**5 + 4*X
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin... | {"variable": "X", "integrand": "-60*X**5 + 4*X", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-10*X**6 + 2*X**2 + C"} | 1 |
construct-rg-simple-integration-l2-s5 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 2 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 5*x**4/2 - 9*x**2/7 + x
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, ... | {"variable": "x", "integrand": "5*x**4/2 - 9*x**2/7 + x", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "x**5/2 - 3*x**3/7 + x**2/2 + C"} | 1 |
construct-rg-simple-integration-l2-s6 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 2 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 20*x**3/7 + 21*x**2 - 14*x
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, co... | {"variable": "x", "integrand": "20*x**3/7 + 21*x**2 - 14*x", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "5*x**4/7 + 7*x**3 - 7*x**2 + C"} | 1 |
construct-rg-simple-integration-l2-s7 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 2 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = -21*X**5/2 + 4*X/3 - 1/4
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos,... | {"variable": "X", "integrand": "-21*X**5/2 + 4*X/3 - 1/4", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-7*X**6/4 + 2*X**2/3 - X/4 + C"} | 1 |
construct-rg-simple-integration-l2-s8 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 2 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = -81*X**4/2 + 4*X
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, as... | {"variable": "X", "integrand": "-81*X**4/2 + 4*X", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-81*X**5/10 + 2*X**2 + C"} | 1 |
construct-rg-simple-integration-l2-s9 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 2 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 20*x**4 + 36*x**3 + 2/3
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, ... | {"variable": "x", "integrand": "20*x**4 + 36*x**3 + 2/3", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "4*x**5 + 9*x**4 + 2*x/3 + C"} | 1 |
construct-rg-simple-integration-l3-s0 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 3 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -2*x**4 - 4*x**3 + 3*x**2
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos... | {"variable": "x", "integrand": "-2*x**4 - 4*x**3 + 3*x**2", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-2*x**5/5 - x**4 + x**3 + C"} | 1 |
construct-rg-simple-integration-l3-s1 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 3 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = 81*X**8/7 + 4*X**7/5 + 7*X**6/2 + 2
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the function... | {"variable": "X", "integrand": "81*X**8/7 + 4*X**7/5 + 7*X**6/2 + 2", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "9*X**9/7 + X**8/10 + X**7/2 + 2*X + C"} | 1 |
construct-rg-simple-integration-l3-s2 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 3 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = -30*X**9 + 28*X**6 + 56*X**3
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, ... | {"variable": "X", "integrand": "-30*X**9 + 28*X**6 + 56*X**3", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-3*X**10 + 4*X**7 + 14*X**4 + C"} | 1 |
construct-rg-simple-integration-l3-s3 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 3 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = 16*X**7 + 54*X**5 + 39*X**2/2
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin,... | {"variable": "X", "integrand": "16*X**7 + 54*X**5 + 39*X**2/2", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "2*X**8 + 9*X**6 + 13*X**3/2 + C"} | 1 |
construct-rg-simple-integration-l3-s4 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 3 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 9*x**8 + 64*x**7/9 - 25*x**4/8 + 1
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions... | {"variable": "x", "integrand": "9*x**8 + 64*x**7/9 - 25*x**4/8 + 1", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "x**9 + 8*x**8/9 - 5*x**5/8 + x + C"} | 1 |
construct-rg-simple-integration-l3-s5 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 3 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = -45*X**8/8 + 12*X**5 + 35*X**4/8
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions s... | {"variable": "X", "integrand": "-45*X**8/8 + 12*X**5 + 35*X**4/8", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-5*X**9/8 + 2*X**6 + 7*X**5/8 + C"} | 1 |
construct-rg-simple-integration-l3-s6 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 3 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 30*x**9 - 14*x**6 - 18*x**3 - 12*x**2
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functi... | {"variable": "x", "integrand": "30*x**9 - 14*x**6 - 18*x**3 - 12*x**2", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "3*x**10 - 2*x**7 - 9*x**4/2 - 4*x**3 + C"} | 1 |
construct-rg-simple-integration-l3-s7 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 3 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = 10*X**9/9 + 16*X**5/3 - 21*X**2/5 - 14*X
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the fun... | {"variable": "X", "integrand": "10*X**9/9 + 16*X**5/3 - 21*X**2/5 - 14*X", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "X**10/9 + 8*X**6/9 - 7*X**3/5 - 7*X**2 + C"} | 1 |
construct-rg-simple-integration-l3-s8 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 3 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = -30*X**9 - 36*X**8 - 80*X**7/9
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin... | {"variable": "X", "integrand": "-30*X**9 - 36*X**8 - 80*X**7/9", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-3*X**10 - 4*X**9 - 10*X**8/9 + C"} | 1 |
construct-rg-simple-integration-l3-s9 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 3 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 9*x**8 - 35*x**6/4 + 45*x**4/8 + x**2/2
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the func... | {"variable": "x", "integrand": "9*x**8 - 35*x**6/4 + 45*x**4/8 + x**2/2", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "x**9 - 5*x**7/4 + 9*x**5/8 + x**3/6 + C"} | 1 |
construct-rg-simple-integration-l4-s0 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 4 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = 40*X**9/3 + 108*X**5/5 - 30*X**4 + 6*X
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the funct... | {"variable": "X", "integrand": "40*X**9/3 + 108*X**5/5 - 30*X**4 + 6*X", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "4*X**10/3 + 18*X**6/5 - 6*X**5 + 3*X**2 + C"} | 1 |
construct-rg-simple-integration-l4-s1 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 4 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = -35*X**9/4 + 72*X**7 + 4*X + 3
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin... | {"variable": "X", "integrand": "-35*X**9/4 + 72*X**7 + 4*X + 3", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-7*X**10/8 + 9*X**8 + 2*X**2 + 3*X + C"} | 1 |
construct-rg-simple-integration-l4-s2 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 4 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 602*x**6/45 + 6*x**2 + 6*x + 6/7
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions s... | {"variable": "x", "integrand": "602*x**6/45 + 6*x**2 + 6*x + 6/7", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "86*x**7/45 + 2*x**3 + 3*x**2 + 6*x/7 + C"} | 1 |
construct-rg-simple-integration-l4-s3 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 4 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = -54*X**8 + 20*X**3 + 24*X**2/5
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin... | {"variable": "X", "integrand": "-54*X**8 + 20*X**3 + 24*X**2/5", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-6*X**9 + 5*X**4 + 8*X**3/5 + C"} | 1 |
construct-rg-simple-integration-l4-s4 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 4 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = 25*X**9/3 - 8*X**5 + 5*X**4
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, c... | {"variable": "X", "integrand": "25*X**9/3 - 8*X**5 + 5*X**4", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "5*X**10/6 - 4*X**6/3 + X**5 + C"} | 1 |
construct-rg-simple-integration-l4-s5 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 4 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 232*x**7/3 - 54*x**5 + 3*x**2
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin,... | {"variable": "x", "integrand": "232*x**7/3 - 54*x**5 + 3*x**2", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "29*x**8/3 - 9*x**6 + x**3 + C"} | 1 |
construct-rg-simple-integration-l4-s6 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 4 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -7*x**6/9 + 6*x**5 - 16*x + 7
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin,... | {"variable": "x", "integrand": "-7*x**6/9 + 6*x**5 - 16*x + 7", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-x**7/9 + x**6 - 8*x**2 + 7*x + C"} | 1 |
construct-rg-simple-integration-l4-s7 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 4 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 45*x**8/2 - 8*x**7 - 28*x**6 - 5*x**4/3 - 18*x
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and t... | {"variable": "x", "integrand": "45*x**8/2 - 8*x**7 - 28*x**6 - 5*x**4/3 - 18*x", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "5*x**9/2 - x**8 - 4*x**7 - x**5/3 - 9*x**2 + C"} | 1 |
construct-rg-simple-integration-l4-s8 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 4 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -60*x**9 - 8*x**3 + 27*x**2 + 3*x/2
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the function... | {"variable": "x", "integrand": "-60*x**9 - 8*x**3 + 27*x**2 + 3*x/2", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-6*x**10 - 2*x**4 + 9*x**3 + 3*x**2/4 + C"} | 1 |
construct-rg-simple-integration-l4-s9 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 4 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 7*x**6 + 15*x**4 - 78*x**2/5
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, ... | {"variable": "x", "integrand": "7*x**6 + 15*x**4 - 78*x**2/5", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "x**7 + 3*x**5 - 26*x**3/5 + C"} | 1 |
construct-rg-simple-integration-l5-s0 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 5 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 63*x**8 - 12*x**5 - 10/x**2 + 27/(8*x**4) - 20/(3*x**5)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and ... | {"variable": "x", "integrand": "63*x**8 - 12*x**5 - 10/x**2 + 27/(8*x**4) - 20/(3*x**5)", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "7*x**9 - 2*x**6 + 3/4 + 10/x - 9/(8*x**3) + 5/(3*x**4) + C"} | 1 |
construct-rg-simple-integration-l5-s1 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 5 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = 15*X**9 + 15*X**6 + 57*X**2/2 + 4/X**5
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the funct... | {"variable": "X", "integrand": "15*X**9 + 15*X**6 + 57*X**2/2 + 4/X**5", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "3*X**10/2 + 15*X**7/7 + 19*X**3/2 - 1/X**4 + C"} | 1 |
construct-rg-simple-integration-l5-s2 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 5 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -9*x**8 + 24*x**7/7 - 49*x**6 + 12/x**3
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the func... | {"variable": "x", "integrand": "-9*x**8 + 24*x**7/7 - 49*x**6 + 12/x**3", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-x**9 + 3*x**8/7 - 7*x**7 - 10 - 6/x**2 + C"} | 1 |
construct-rg-simple-integration-l5-s3 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 5 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = -8*X**7/63 + 15*X**5/2 - 10*X**4/3 - 3/X**4 + 20/X**6
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi... | {"variable": "X", "integrand": "-8*X**7/63 + 15*X**5/2 - 10*X**4/3 - 3/X**4 + 20/X**6", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-X**8/63 + 5*X**6/4 - 2*X**5/3 + X**(-3) - 4/X**5 + C"} | 1 |
construct-rg-simple-integration-l5-s4 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 5 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = 20*X**9 + 14*X**6 + 4*X**3/3 + 25/(2*X**6)
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the f... | {"variable": "X", "integrand": "20*X**9 + 14*X**6 + 4*X**3/3 + 25/(2*X**6)", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "2*X**10 + 2*X**7 + X**4/3 + 5/4 - 5/(2*X**5) + C"} | 1 |
construct-rg-simple-integration-l5-s5 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 5 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = -10*X**7 - 9*X**2 - 7*X
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, ... | {"variable": "X", "integrand": "-10*X**7 - 9*X**2 - 7*X", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-5*X**8/4 - 3*X**3 - 7*X**2/2 - 6 + C"} | 1 |
construct-rg-simple-integration-l5-s6 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 5 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = -8*X + 3/(2*X**2) + 2/X**4 - 50/X**6
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functio... | {"variable": "X", "integrand": "-8*X + 3/(2*X**2) + 2/X**4 - 50/X**6", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-4*X**2 + 5 - 3/(2*X) - 2/(3*X**3) + 10/X**5 + C"} | 1 |
construct-rg-simple-integration-l5-s7 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 5 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = 14*X**6 - 30*X**4 + 36*X**3 - 3/X**2 - 20/X**3 - 35/X**6
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and... | {"variable": "X", "integrand": "14*X**6 - 30*X**4 + 36*X**3 - 3/X**2 - 20/X**3 - 35/X**6", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "2*X**7 - 6*X**5 + 9*X**4 + 3/X + 10/X**2 + 7/X**5 + C"} | 1 |
construct-rg-simple-integration-l5-s8 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 5 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = -9*X**8/5 + 4*X**7 - 7*X**6 + 24*X**3 + 2/3
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the ... | {"variable": "X", "integrand": "-9*X**8/5 + 4*X**7 - 7*X**6 + 24*X**3 + 2/3", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-X**9/5 + X**8/2 - X**7 + 6*X**4 + 2*X/3 + C"} | 1 |
construct-rg-simple-integration-l5-s9 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 5 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 185*x**9/6 - 6*x**5 + 5*x/2 - 32/x**5
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functi... | {"variable": "x", "integrand": "185*x**9/6 - 6*x**5 + 5*x/2 - 32/x**5", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "37*x**10/12 - x**6 + 5*x**2/4 + 8/x**4 + C"} | 1 |
construct-rg-simple-integration-l6-s0 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 6 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -45*x**8/7 - 12*x**3/7 + 7/x**2 + 4/x**3 + 20/(3*x**6)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and p... | {"variable": "x", "integrand": "-45*x**8/7 - 12*x**3/7 + 7/x**2 + 4/x**3 + 20/(3*x**6)", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-5*x**9/7 - 3*x**4/7 - 7/x - 2/x**2 - 4/(3*x**5) + C"} | 1 |
construct-rg-simple-integration-l6-s1 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 6 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -16*x**7/5 + 5/(3*x**2) - 4/x**3 + 2/x**5 + 60/x**7 + 20/x**11
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants... | {"variable": "x", "integrand": "-16*x**7/5 + 5/(3*x**2) - 4/x**3 + 2/x**5 + 60/x**7 + 20/x**11", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-2*x**8/5 - 1/5 - 5/(3*x) + 2/x**2 - 1/(2*x**4) - 10/x**6 - 2/x**10 + C"} | 1 |
construct-rg-simple-integration-l6-s2 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 6 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = 63*X**6 - 16*X**3 + 6/X**4 - 6/X**5 - 45/X**6 + 6/X**7 + 20/(7*X**11)
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the co... | {"variable": "X", "integrand": "63*X**6 - 16*X**3 + 6/X**4 - 6/X**5 - 45/X**6 + 6/X**7 + 20/(7*X**11)", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "9*X**7 - 4*X**4 - 2/X**3 + 3/(2*X**4) + 9/X**5 - 1/X**6 - 2/(7*X**10) + C"} | 1 |
construct-rg-simple-integration-l6-s3 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 6 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -25*x**9/4 - 3*x**2 - 14*x + 7/(2*x**2) + 2/x**3 + 9/(2*x**6) + 63/x**8
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the ... | {"variable": "x", "integrand": "-25*x**9/4 - 3*x**2 - 14*x + 7/(2*x**2) + 2/x**3 + 9/(2*x**6) + 63/x**8", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-5*x**10/8 - x**3 - 7*x**2 - 7/(2*x) - 1/x**2 - 9/(10*x**5) - 9/x**7 + C"} | 1 |
construct-rg-simple-integration-l6-s4 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 6 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = -333*X**8/40 - 14*X**6 - 9/X**2 - 21/(2*X**4) - 12/X**5 + 36/X**10
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the const... | {"variable": "X", "integrand": "-333*X**8/40 - 14*X**6 - 9/X**2 - 21/(2*X**4) - 12/X**5 + 36/X**10", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-37*X**9/40 - 2*X**7 + 9/X + 7/(2*X**3) + 3/X**4 - 4/X**9 + C"} | 1 |
construct-rg-simple-integration-l6-s5 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 6 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -144*x**11/5 + 517*x**10/10 + 18*x**8 + 20/x**11
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and... | {"variable": "x", "integrand": "-144*x**11/5 + 517*x**10/10 + 18*x**8 + 20/x**11", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-12*x**12/5 + 47*x**11/10 + 2*x**9 - 2/x**10 + C"} | 1 |
construct-rg-simple-integration-l6-s6 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 6 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = 33*X**10 - 70*X**6 - 12*X - 8 - 2/(5*X**2) - 129/(20*X**7)
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E a... | {"variable": "X", "integrand": "33*X**10 - 70*X**6 - 12*X - 8 - 2/(5*X**2) - 129/(20*X**7)", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "3*X**11 - 10*X**7 - 6*X**2 - 8*X + 2/(5*X) + 43/(40*X**6) + C"} | 1 |
construct-rg-simple-integration-l6-s7 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 6 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(X) of
f(X) = 18*X**5 + 5*X**2 - 2 - 10/X**2 + 4/X**9 - 27/X**10 + 25/(4*X**11)
i.e. any F with dF/dX = f(X).
Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the consta... | {"variable": "X", "integrand": "18*X**5 + 5*X**2 - 2 - 10/X**2 + 4/X**9 - 27/X**10 + 25/(4*X**11)", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "3*X**6 + 5*X**3/3 - 2*X + 10/X - 1/(2*X**8) + 3/X**9 - 5/(8*X**10) + C"} | 1 |
construct-rg-simple-integration-l6-s8 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 6 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 45*x**9 - 30*x**4/7 - 18*x - 9/x**4 + 16/(3*x**5) + 24/x**7 - 81/x**10
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the c... | {"variable": "x", "integrand": "45*x**9 - 30*x**4/7 - 18*x - 9/x**4 + 16/(3*x**5) + 24/x**7 - 81/x**10", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "9*x**10/2 - 6*x**5/7 - 9*x**2 + 3/x**3 - 4/(3*x**4) - 4/x**6 + 9/x**9 + C"} | 1 |
construct-rg-simple-integration-l6-s9 | construct | rg_simple_integration | symbolic_antiderivative_polynomial | analysis | competition | 6 | ReasoningGym/simple_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 108*x**11 + 60*x**9 - 27*x**8/10 + 8*x**7 + 28*x**6/5 + 30/x**6 + 81/(7*x**10)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parenthese... | {"variable": "x", "integrand": "108*x**11 + 60*x**9 - 27*x**8/10 + 8*x**7 + 28*x**6/5 + 30/x**6 + 81/(7*x**10)", "family": "rg_simple_integration", "subset": "construct"} | null | null | null | {"antiderivative": "9*x**12 + 6*x**10 - 3*x**9/10 + x**8 + 4*x**7/5 - 6/x**5 - 9/(7*x**9) + C"} | 1 |
construct-rlve-antiderivative-l1-s0 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 1 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = 2*x
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, and the functio... | {"f_prime": "2*x", "max_ops": 24, "max_len": 480, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "x**2"} | 1 |
construct-rlve-antiderivative-l1-s1 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 1 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = 64*x**3
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, and the fun... | {"f_prime": "64*x**3", "max_ops": 28, "max_len": 540, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "16*x**4"} | 1 |
construct-rlve-antiderivative-l1-s2 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 1 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = exp(sin(x))*cos(x)
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, ... | {"f_prime": "exp(sin(x))*cos(x)", "max_ops": 28, "max_len": 620, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "exp(sin(x))"} | 1 |
construct-rlve-antiderivative-l1-s3 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 1 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = 1/(2*x)
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, and the fun... | {"f_prime": "1/(2*x)", "max_ops": 28, "max_len": 560, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "log(x)/2"} | 1 |
construct-rlve-antiderivative-l1-s4 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 1 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = cos(x + 1)
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, and the ... | {"f_prime": "cos(x + 1)", "max_ops": 28, "max_len": 600, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "sin(x + 1)"} | 1 |
construct-rlve-antiderivative-l1-s5 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 1 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = 1/(12*x**(3/4))
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, and... | {"f_prime": "1/(12*x**(3/4))", "max_ops": 32, "max_len": 600, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "x**(1/4)/3"} | 1 |
construct-rlve-antiderivative-l1-s6 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 1 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = cos(x)*cos(sin(x))
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, ... | {"f_prime": "cos(x)*cos(sin(x))", "max_ops": 28, "max_len": 620, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "sin(sin(x))"} | 1 |
construct-rlve-antiderivative-l1-s7 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 1 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = x**x*(log(x) + 1)
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, a... | {"f_prime": "x**x*(log(x) + 1)", "max_ops": 24, "max_len": 480, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "x**x"} | 1 |
construct-rlve-antiderivative-l1-s8 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 1 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = cos(x)/(4*sin(x)**(3/4))
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parenth... | {"f_prime": "cos(x)/(4*sin(x)**(3/4))", "max_ops": 32, "max_len": 660, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "sin(x)**(1/4)"} | 1 |
construct-rlve-antiderivative-l1-s9 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 1 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = -4*x**3*sin(x**4)
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, a... | {"f_prime": "-4*x**3*sin(x**4)", "max_ops": 28, "max_len": 580, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "cos(x**4)"} | 1 |
construct-rlve-antiderivative-l2-s0 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 2 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = 7/(12*x**(5/12))
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, an... | {"f_prime": "7/(12*x**(5/12))", "max_ops": 28, "max_len": 580, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "x**(7/12)"} | 1 |
construct-rlve-antiderivative-l2-s1 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 2 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = 1 - exp(x)
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, and the ... | {"f_prime": "1 - exp(x)", "max_ops": 32, "max_len": 680, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "x - exp(x) + 2"} | 1 |
construct-rlve-antiderivative-l2-s2 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 2 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = x*cos(x)/sin(x) + log(sin(x))
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and pa... | {"f_prime": "x*cos(x)/sin(x) + log(sin(x))", "max_ops": 32, "max_len": 680, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "log(sin(x)**x)"} | 1 |
construct-rlve-antiderivative-l2-s3 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 2 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = 4*x
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, and the functio... | {"f_prime": "4*x", "max_ops": 28, "max_len": 520, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "2*x**2"} | 1 |
construct-rlve-antiderivative-l2-s4 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 2 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = cos(x) + 1
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, and the ... | {"f_prime": "cos(x) + 1", "max_ops": 32, "max_len": 680, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "x + sin(x) + 1"} | 1 |
construct-rlve-antiderivative-l2-s5 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 2 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = (2*x)**x*(log(2*x) + 1)
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parenthe... | {"f_prime": "(2*x)**x*(log(2*x) + 1)", "max_ops": 28, "max_len": 560, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "(2*x)**x"} | 1 |
construct-rlve-antiderivative-l2-s6 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 2 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = 8*x
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, and the functio... | {"f_prime": "8*x", "max_ops": 32, "max_len": 600, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "4*x**2 - 1"} | 1 |
construct-rlve-antiderivative-l2-s7 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 2 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = x*(2*x + 4) + (x + 2)**2
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parenth... | {"f_prime": "x*(2*x + 4) + (x + 2)**2", "max_ops": 32, "max_len": 640, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "x*(x + 2)**2"} | 1 |
construct-rlve-antiderivative-l2-s8 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 2 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = 3*sin(x - 1)*sin(cos(x - 1))*cos(cos(x - 1))**2
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals,... | {"f_prime": "3*sin(x - 1)*sin(cos(x - 1))*cos(cos(x - 1))**2", "max_ops": 36, "max_len": 760, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "cos(cos(x - 1))**3"} | 1 |
construct-rlve-antiderivative-l2-s9 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 2 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = -exp(x) - 3
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, and the... | {"f_prime": "-exp(x) - 3", "max_ops": 36, "max_len": 660, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "-3*x - exp(x)"} | 1 |
construct-rlve-antiderivative-l3-s0 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 3 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = (x*cos(x) + sin(x))*sin(x*sin(x))*sin(sin(cos(x*sin(x))))*cos(cos(x*sin(x)))
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the ... | {"f_prime": "(x*cos(x) + sin(x))*sin(x*sin(x))*sin(sin(cos(x*sin(x))))*cos(cos(x*sin(x)))", "max_ops": 40, "max_len": 860, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "cos(sin(cos(x*sin(x))))"} | 1 |
construct-rlve-antiderivative-l3-s1 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 3 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = -x**3*exp(x/4)*sin(exp(x/4))/4 + 3*x**2*cos(exp(x/4))
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer lit... | {"f_prime": "-x**3*exp(x/4)*sin(exp(x/4))/4 + 3*x**2*cos(exp(x/4))", "max_ops": 40, "max_len": 760, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "x**3*cos(exp(x/4))"} | 1 |
construct-rlve-antiderivative-l3-s2 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 3 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = 4*x + 1/sqrt(x)
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, and... | {"f_prime": "4*x + 1/sqrt(x)", "max_ops": 44, "max_len": 760, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "2*sqrt(x) + 2*x**2"} | 1 |
construct-rlve-antiderivative-l3-s3 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 3 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = -sin(x)
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, and the fun... | {"f_prime": "-sin(x)", "max_ops": 24, "max_len": 520, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "cos(x)"} | 1 |
construct-rlve-antiderivative-l3-s4 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 3 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = -x*sin(x) + cos(x) - 1
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parenthes... | {"f_prime": "-x*sin(x) + cos(x) - 1", "max_ops": 36, "max_len": 720, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "x*cos(x) - x - 2"} | 1 |
construct-rlve-antiderivative-l3-s5 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 3 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = (x**2/cos(x))**(1/4)*(x**2*sin(x)/(4*cos(x)**2) + x/(2*cos(x)))*cos(x)/x**2
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the v... | {"f_prime": "(x**2/cos(x))**(1/4)*(x**2*sin(x)/(4*cos(x)**2) + x/(2*cos(x)))*cos(x)/x**2", "max_ops": 40, "max_len": 800, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "(x**2/cos(x))**(1/4)"} | 1 |
construct-rlve-antiderivative-l3-s6 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 3 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = -sin(x - 3)
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, and the... | {"f_prime": "-sin(x - 3)", "max_ops": 28, "max_len": 600, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "cos(x - 3)"} | 1 |
construct-rlve-antiderivative-l3-s7 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 3 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = -4*x*sin(2*x**2)*cos(cos(2*x**2))/3
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** ... | {"f_prime": "-4*x*sin(2*x**2)*cos(cos(2*x**2))/3", "max_ops": 40, "max_len": 760, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "sin(cos(2*x**2))/3"} | 1 |
construct-rlve-antiderivative-l3-s8 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 3 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = 1/x
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, and the functio... | {"f_prime": "1/x", "max_ops": 28, "max_len": 560, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "log(3*x)"} | 1 |
construct-rlve-antiderivative-l3-s9 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 3 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = -sin(2*x)/2 - 1
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, and... | {"f_prime": "-sin(2*x)/2 - 1", "max_ops": 36, "max_len": 700, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "-x + cos(2*x)/4"} | 1 |
construct-rlve-antiderivative-l4-s0 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 4 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = -(-16*x + 16*sin(x))**x*(x*(16*cos(x) - 16)/(-16*x + 16*sin(x)) + log(-16*x + 16*sin(x)))*sin((-16*x + 16*sin(x))**x)
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as ... | {"f_prime": "-(-16*x + 16*sin(x))**x*(x*(16*cos(x) - 16)/(-16*x + 16*sin(x)) + log(-16*x + 16*sin(x)))*sin((-16*x + 16*sin(x))**x)", "max_ops": 44, "max_len": 940, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "cos((-16*x + 16*sin(x))**x)"} | 1 |
construct-rlve-antiderivative-l4-s1 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 4 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = 36*x + 6
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, and the fu... | {"f_prime": "36*x + 6", "max_ops": 40, "max_len": 740, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "18*x**2 + 6*x - 2"} | 1 |
construct-rlve-antiderivative-l4-s2 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 4 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = 2 - 6*x**2
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, and the ... | {"f_prime": "2 - 6*x**2", "max_ops": 40, "max_len": 740, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "-2*x**3 + 2*x + 2"} | 1 |
construct-rlve-antiderivative-l4-s3 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 4 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = (x**2*cos(x)/sin(x) + 2*x*log(sin(x)))*sin(x)**(x**2)
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer lit... | {"f_prime": "(x**2*cos(x)/sin(x) + 2*x*log(sin(x)))*sin(x)**(x**2)", "max_ops": 32, "max_len": 680, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "sin(x)**(x**2)"} | 1 |
construct-rlve-antiderivative-l4-s4 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 4 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = -12*sqrt(x) + 3*x*(-16 - 2/sqrt(x)) - 48*x
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - ... | {"f_prime": "-12*sqrt(x) + 3*x*(-16 - 2/sqrt(x)) - 48*x", "max_ops": 52, "max_len": 860, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "3*x*(-4*sqrt(x) - 16*x)"} | 1 |
construct-rlve-antiderivative-l4-s5 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 4 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = (2 - 3*cos(x))*sin(x) + (2*x - 3*sin(x))*cos(x)
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals,... | {"f_prime": "(2 - 3*cos(x))*sin(x) + (2*x - 3*sin(x))*cos(x)", "max_ops": 44, "max_len": 860, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "(2*x - 3*sin(x))*sin(x)"} | 1 |
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