[User]
Find the number of times the graphs of f(x) = -1cos(3π(3|(3x^2 + 4x - 5) - 1| + 1) - 2) and g(x) = 1cos(2π(5x + 1)) - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3|((-1(-2x - 5))/(3(-2x - 5) - 2)) - 3| + 1 and g(x) = (3(-3cos(1πx + 2) - 2) + 2)/(-1(-3cos(1πx + 2) - 2) - 1) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3|(-1sin(2π(2|x + 2| - 1) + 3)) + 3| + 3 = -2(2x - 1)^2 - 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -4(3|(-2x - 5)| - 3)^2 - 2(3|(-2x - 5)| - 3) + 4 and g(x) = -2|(-1sin(3πx + 1) + 1)| - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2cos(1π(3(-5x^2 + 1) + 5) - 1) - 1 and g(x) = 4(-2|x - 1| - 1) + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1cos(1π(1((-1x - 2)/(-3x - 3))^2 - 2((-1x - 2)/(-3x - 3)) - 4) + 3) - 3 = -2(3|x - 3| - 3)^2 + 1(3|x - 3| - 3) - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1e^(1(-3|(2|x + 2| + 3) - 3| - 2)) - 3 and g(x) = 2sin(1π(-3x^2 + 3x + 1) - 1) - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1((2(-1|x - 1| - 1) + 2)/(1(-1|x - 1| - 1))) + 2 = 3|(-5x^2 + 3x + 4)| have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2e^(-1(1|(-1|x| - 2) + 2| - 2)) + 1 and g(x) = 2sin(1π((-2x + 1)/(-1x - 2)) - 2) - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -5((3((2x - 3)/(3x + 1)) + 2)/(-1((2x - 3)/(3x + 1)) + 3)) + 5 and g(x) = -3(-3cos(1πx - 1) - 1) - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1|(-1(-1sin(1πx - 1) - 2)^2 - 2(-1sin(1πx - 1) - 2) + 3) - 3| + 1 = -3e^(2(-1|x + 2| + 3)) + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-1(-3(-3x)^2 + 5(-3x) + 5) + 3)/(3(-3(-3x)^2 + 5(-3x) + 5) + 2) = -3|((3x - 3)/(2x + 2)) - 3| + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3cos(3π((-1(-2|x - 3| + 2) - 2)/(3(-2|x - 3| + 2) - 2)) - 3) - 1 and g(x) = (-1((2x - 3)/(1x + 2)) - 2)/(2((2x - 3)/(1x + 2)) - 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2cos(1π(2(-1x + 4) - 1)) and g(x) = (2((-1x - 2)/(1x)) + 3)/(-2((-1x - 2)/(1x)) - 3) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2|(-1cos(1π(-3|x - 2|) - 1) - 3) + 3| - 3 = -2|((2x + 3)/(-1x + 2)) + 3| - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3|((1((-3x - 1)/(2x + 1)))/(1((-3x - 1)/(2x + 1))))| = -1(3cos(2πx + 2) - 3) - 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2cos(3π((-1((-2x + 1)/(-1x - 3)) + 2)/(-2((-2x + 1)/(-1x - 3)))) - 2) - 3 and g(x) = -3|(3x^2 + 1x - 4) + 1| - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (2(2sin(1π(4x) + 2) - 2) - 3)/(2(2sin(1π(4x) + 2) - 2) + 1) = -5(-4x - 4) + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2cos(1π(-5(-4x + 1)^2 - 5) + 1) + 2 = 5(-3cos(3πx - 3) + 3)^2 + 3(-3cos(3πx - 3) + 3) - 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3|(-2|(-1|x - 2| + 3) - 2| + 3) + 1| + 3 = (3(5x + 5) - 2)/(-2(5x + 5) + 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3cos(3π(1|((2x + 2)/(1x - 2)) + 2|) - 3) - 2 and g(x) = -3cos(1π(3|x - 3| + 2)) + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1(3(-3sin(3πx + 3) - 2) + 5) + 1 = 2|(4x^2 - 3x - 4) - 1| + 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2|(-1|((3x + 2)/(1x)) + 3| + 1) + 2| + 2 and g(x) = -3(4x^2 - 5x - 5) - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2|(1(-3cos(1πx + 1) + 2)) + 2| + 2 and g(x) = -3|(2sin(1πx - 3))| + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (2(2|(3sin(3πx - 3) + 2) - 3| - 3))/(1(2|(3sin(3πx - 3) + 2) - 3| - 3)) and g(x) = 5(-2sin(3πx - 1)) + 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1e^(1(-2|(2x^2 - 2x - 2) + 1| - 2)) - 1 and g(x) = 1cos(2π(1x^2 - 2x - 3)) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 4(-2|(5x - 3) - 2| - 3)^2 - 1(-2|(5x - 3) - 2| - 3) + 2 and g(x) = (-1(-1cos(2πx + 3)) + 1)/(2(-1cos(2πx + 3)) + 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1|(-2(-1sin(2πx - 3) - 1) + 3) + 1| + 2 = 2|(-3e^(-1x) - 1) - 2| + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3sin(2π(-1(-2x^2 + 3x)^2 - 1(-2x^2 + 3x) - 3) - 3) - 2 and g(x) = 3(-1x + 1) + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-1(2cos(2π(-2x + 3) - 2) - 3) - 3)/(2(2cos(2π(-2x + 3) - 2) - 3) + 2) and g(x) = 3sin(3π(1x^2 + 1x + 1) - 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-3((3(3cos(3πx + 3) + 3))/(-2(3cos(3πx + 3) + 3) - 2)) + 2)/(3((3(3cos(3πx + 3) + 3))/(-2(3cos(3πx + 3) + 3) - 2))) and g(x) = -1(1cos(3πx + 2) - 2) - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2(4(1cos(1πx - 3) + 1)^2 - 2(1cos(1πx - 3) + 1) + 3)^2 - 3(4(1cos(1πx - 3) + 1)^2 - 2(1cos(1πx - 3) + 1) + 3) - 4 and g(x) = 2sin(3π(-2x^2 + 3x - 3) + 1) + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1(-4(3cos(2πx + 1) - 3)^2 - 2(3cos(2πx + 1) - 3) - 4)^2 - 2(-4(3cos(2πx + 1) - 3)^2 - 2(3cos(2πx + 1) - 3) - 4) - 2 and g(x) = -3((-1x)/(-1x - 2))^2 - 4((-1x)/(-1x - 2)) - 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(-1sin(3π(-4x - 4) - 2) + 2)^2 - 5(-1sin(3π(-4x - 4) - 2) + 2) + 4 = (-1(-2|x - 1| - 1) + 2)/(3(-2|x - 1| - 1) - 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2|((-1(-2x^2 - 5x + 2) + 1)/(-2(-2x^2 - 5x + 2) + 3)) + 1| - 3 and g(x) = -4((-1x - 3)/(-1x - 3))^2 + 3((-1x - 3)/(-1x - 3)) - 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1(-3(-1x^2 + 4x + 1))^2 - 4(-3(-1x^2 + 4x + 1)) - 1 and g(x) = 3(-3x^2 + 5x + 4)^2 + 2(-3x^2 + 5x + 4) - 5 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3(5(-1cos(2πx + 2))^2 + 2(-1cos(2πx + 2)) - 2) - 2 and g(x) = -1|(-3cos(2πx - 2) - 1)| - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3sin(1π(-1(1x - 3)^2 - 5(1x - 3) - 2) - 1) + 3 = -2sin(1π(-3|x + 3| - 3) - 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (1(3|((-3x - 2)/(2x)) + 1| + 3) + 1)/(-1(3|((-3x - 2)/(2x)) + 1| + 3) - 2) and g(x) = -2(-2x^2 + 2x + 4)^2 + 1(-2x^2 + 2x + 4) + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3(-1|(-2x + 2) + 2| + 1) - 3 and g(x) = -3sin(2π(-5x^2 - 1x - 4) - 1) + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2|((2((1x - 2)/(-2x - 3)) + 1)/(-1((1x - 2)/(-2x - 3)))) - 3| + 1 and g(x) = -3sin(2π(-1x^2 + 1x) + 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-3(1(1|x| - 3)^2 - 2) - 1)/(2(1(1|x| - 3)^2 - 2) + 3) and g(x) = -2cos(1π((-2x - 3)/(-2x - 1)) + 3) + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3(-1|(2|x - 3| + 1) - 1| + 3)^2 - 5(-1|(2|x - 3| + 1) - 1| + 3) - 4 and g(x) = 2sin(3π((-3x + 2)/(-1x - 2)) - 2) - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3sin(3π(-4(5x + 1)^2 + 1(5x + 1) + 4) + 3) - 3 = (-2((2x)/(-3x - 3)) + 1)/(3((2x)/(-3x - 3))) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -5(-2(4x^2 - 5x - 1)^2 + 2(4x^2 - 5x - 1) + 2)^2 - 3(-2(4x^2 - 5x - 1)^2 + 2(4x^2 - 5x - 1) + 2) + 4 and g(x) = (-3(-5x) - 2)/(-1(-5x)) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1(4(-2cos(1πx - 2) + 3) - 3)^2 + 3(4(-2cos(1πx - 2) + 3) - 3) - 1 = -3|(-1e^(1x))| have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(2cos(3π(-2|x + 1| + 3) - 2) + 3)^2 + 1(2cos(3π(-2|x + 1| + 3) - 2) + 3) + 3 = 3(5x^2 + 3x - 5)^2 - 5(5x^2 + 3x - 5) + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2sin(2π(5((3x - 3)/(-1x - 2)) - 4) - 1) = 2cos(1π(4x - 3) + 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3e^(2(-3|(-2x + 3) - 2| + 2)) - 3 and g(x) = -4(-2cos(1πx) - 1) - 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3|((-2(-2e^(-2x) + 2) + 1)/(2(-2e^(-2x) + 2) + 2))| - 2 and g(x) = -1|(-2cos(3πx - 1) + 3) - 3| - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -5(-2cos(3π(2|x - 1| + 1) + 2) - 2)^2 + 1(-2cos(3π(2|x - 1| + 1) + 2) - 2) + 3 = -5(-1e^(2x) + 2) - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (2(1(-2x^2 - 2x + 3)^2 - 4(-2x^2 - 2x + 3) - 2) + 2)/(-1(1(-2x^2 - 2x + 3)^2 - 4(-2x^2 - 2x + 3) - 2) + 3) and g(x) = -5(1x^2 - 4x + 1)^2 - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(3cos(3π(2x + 5) + 3) - 2) + 2 = 1(2sin(2πx) - 3) + 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3cos(3π(-3|(-3x^2 + 4x - 2) - 1| + 3)) and g(x) = 2(3x^2 + 1x - 1)^2 - 1(3x^2 + 1x - 1) - 5 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1|(4(-1cos(2πx))^2 + 5(-1cos(2πx)) - 5) + 1| - 3 and g(x) = 1(-1x + 4) - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-2(3(2sin(2πx - 2) + 1) - 3) - 3)/(-2(3(2sin(2πx - 2) + 1) - 3) - 2) = -1(3x - 2)^2 - 2(3x - 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (1(-1cos(1π((2x + 3)/(3x + 1)) - 3) - 1) + 2)/(-3(-1cos(1π((2x + 3)/(3x + 1)) - 3) - 1) - 1) and g(x) = -5(-1sin(2πx + 2) + 3) + 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1|(1|(-3x + 4) + 3| + 2) + 1| - 1 and g(x) = -5(1sin(1πx + 2) + 1)^2 - 1(1sin(1πx + 2) + 1) + 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3(-5((2x - 3)/(2x + 3))^2 + 3((2x - 3)/(2x + 3)) - 5)^2 - 2(-5((2x - 3)/(2x + 3))^2 + 3((2x - 3)/(2x + 3)) - 5) + 3 and g(x) = (3(-3cos(3πx - 2) + 3) + 2)/(3(-3cos(3πx - 2) + 3) - 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3cos(2π((1(-2x^2 + 3x - 1) - 2)/(-3(-2x^2 + 3x - 1) - 2)) + 2) - 1 and g(x) = 5(-3cos(3πx - 3) + 1) - 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2|(-2|(3x^2 + 1x + 4) - 1| - 1) - 1| + 2 and g(x) = -2(3sin(3πx) - 2)^2 - 2(3sin(3πx) - 2) + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2((-2(2sin(3πx + 1) + 1) + 1)/(-3(2sin(3πx + 1) + 1) - 3))^2 - 3((-2(2sin(3πx + 1) + 1) + 1)/(-3(2sin(3πx + 1) + 1) - 3)) - 5 and g(x) = 5(2|x + 3| - 2) + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3sin(1π(2(-3x^2 + 4x)^2)) - 2 and g(x) = 5((2x - 3)/(2x + 3))^2 - 2((2x - 3)/(2x + 3)) - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3(-2sin(2π((2x)/(-1x - 3)) - 1)) - 4 = (1(-1sin(3πx + 2) - 1) - 2)/(2(-1sin(3πx + 2) - 1) + 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (3((3(-4x^2 + 1x - 3))/(-1(-4x^2 + 1x - 3) - 3)) + 3)/(2((3(-4x^2 + 1x - 3))/(-1(-4x^2 + 1x - 3) - 3)) + 2) and g(x) = -3sin(1π(-2|x + 1| - 2) + 3) + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1((3(-1sin(3πx + 3)) - 2)/(2(-1sin(3πx + 3)) - 1)) - 1 and g(x) = -4(4x^2 + 2x + 5) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -5((-2(2sin(3πx - 1) - 3) - 3)/(1(2sin(3πx - 1) - 3) + 2))^2 - 4((-2(2sin(3πx - 1) - 3) - 3)/(1(2sin(3πx - 1) - 3) + 2)) + 3 = (3(3cos(3πx) - 2) - 3)/(-3(3cos(3πx) - 2) - 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2|(-2cos(2π((-3x - 3)/(-2x + 3)) + 3) - 3) + 2| - 3 and g(x) = 1|((1x + 2)/(3x)) + 3| - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3cos(1π((1(3x^2 + 3x - 4) + 1)/(-1(3x^2 + 3x - 4))) + 3) - 1 and g(x) = -5(1e^(2x) - 3) + 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3(-5(-1x^2 - 4x + 2) - 4)^2 + 5(-5(-1x^2 - 4x + 2) - 4) - 2 and g(x) = (-2(1sin(1πx - 1) - 3) - 3)/(3(1sin(1πx - 1) - 3) - 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-3(-2cos(1π(2x - 2) - 1) + 1) - 2)/(-1(-2cos(1π(2x - 2) - 1) + 1) + 3) and g(x) = 1sin(3π(5x^2 - 3)) + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (3(-1|(-3cos(2πx - 1) - 1)| + 2) - 1)/(1(-1|(-3cos(2πx - 1) - 1)| + 2) + 1) and g(x) = 3(-2cos(2πx - 2) + 2)^2 + 3(-2cos(2πx - 2) + 2) + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1(3(-2sin(3πx - 3)) - 2) - 3 = 2|(-2cos(1πx + 2) + 1) - 2| - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3cos(3π(2|(-1x + 4)| + 2)) - 2 = -2cos(1π(4x + 5) - 1) - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-1(-2sin(2π(-2x^2 - 4x + 1) + 3)) - 3)/(-3(-2sin(2π(-2x^2 - 4x + 1) + 3)) - 3) and g(x) = 1(3sin(2πx + 3) + 1)^2 - 1(3sin(2πx + 3) + 1) - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1|(3sin(2π(-1|x + 3|) + 2) - 1) - 2| - 2 and g(x) = (-2(-3x + 4) - 1)/(-1(-3x + 4) + 3) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3cos(3π((-2(-3|x - 2| + 2) - 1)/(3(-3|x - 2| + 2) + 3)) + 1) = 3sin(2π((-2x - 3)/(-1x)) - 2) + 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(1(-1cos(3πx + 2) - 2) - 1)^2 + 5(1(-1cos(3πx + 2) - 2) - 1) + 3 = -3((3x + 1)/(2x - 1)) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (1(4(-3cos(3πx + 2) + 2) + 4) - 2)/(1(4(-3cos(3πx + 2) + 2) + 4) - 2) = -2cos(3π(-3|x + 3| + 2) + 3) + 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1(1|(-3|x - 3| + 3) - 3|) - 5 and g(x) = 4(3|x + 2| - 3)^2 - 2(3|x + 2| - 3) + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1(3cos(3π(-2|x - 2| + 2) + 1) + 1) - 5 and g(x) = -2(-3sin(1πx - 3) + 3)^2 + 2(-3sin(1πx - 3) + 3) - 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2|((-3(1|x| - 3) - 3)/(-3(1|x| - 3))) - 1| + 2 and g(x) = 1|(-1|x + 3| - 3) - 2| in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1sin(1π((-2(-3x^2 - 3x - 4) + 2)/(-1(-3x^2 - 3x - 4) + 3)) - 1) - 3 = 2sin(2π(3|x - 1| - 3) + 1) - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1(-3|(2sin(1πx - 3) + 3) + 1| + 1)^2 - 4(-3|(2sin(1πx - 3) + 3) + 1| + 1) - 4 = -2|(3|x + 2| + 1) - 2| - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3|((-1(3e^(-1x) + 1) + 1)/(2(3e^(-1x) + 1)))| = 3sin(1π(2x - 5) + 3) - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3|(-1(-1x - 3) + 5) + 2| = 2(-2sin(1πx - 3) + 2)^2 + 5(-2sin(1πx - 3) + 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3cos(1π(4(-3x^2 + 2x + 3)^2 - 2(-3x^2 + 2x + 3) + 5) + 1) + 3 and g(x) = 3|((-2x + 3)/(3x - 2))| + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1sin(2π(-5(2x^2 - 2x - 3)^2 + 5(2x^2 - 2x - 3) + 1) + 1) - 1 and g(x) = 5(2cos(1πx + 1) - 3)^2 + 3(2cos(1πx + 1) - 3) - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3(5(2x + 2)^2 - 2(2x + 2) - 4)^2 - 3 and g(x) = -2|(1|x - 2| + 3) + 3| - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3(-2(-3sin(2πx - 2) + 2)) - 2 = -3((-1x + 3)/(1x + 2)) - 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2(3(-1cos(1πx + 1))^2 + 2(-1cos(1πx + 1)) - 4) - 4 and g(x) = 1cos(3π(-1|x - 2| + 2) + 1) - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1sin(1π(5(-1|x| + 3)^2 + 3(-1|x| + 3)) - 2) and g(x) = 3sin(1π(1x + 5) + 2) - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1sin(3π(-1(-4x + 3) - 3) - 3) and g(x) = (3((-3x - 2)/(2x - 3)))/(2((-3x - 2)/(2x - 3)) + 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(1|(1x^2 - 4) + 2| - 3)^2 - 2(1|(1x^2 - 4) + 2| - 3) - 2 = -2cos(1π(-2x + 1) - 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (1(3(-3sin(2πx + 2) - 2)^2 + 3(-3sin(2πx + 2) - 2) - 4) - 2)/(2(3(-3sin(2πx + 2) - 2)^2 + 3(-3sin(2πx + 2) - 2) - 4) + 2) and g(x) = 1cos(1π((1x - 3)/(1x + 1)) + 1) + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -4(-1(-4x + 1)^2 - 4(-4x + 1) + 3)^2 + 2(-1(-4x + 1)^2 - 4(-4x + 1) + 3) and g(x) = -3|((2x - 3)/(-3x + 1)) - 1| where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1|(-3cos(3π(-4x - 2) + 3) + 3) - 1| - 2 = (2(-2sin(3πx + 3) + 2) + 3)/(-2(-2sin(3πx + 3) + 2) + 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1cos(1π(1((-1x + 1)/(2x - 1)) - 3) + 3) + 2 and g(x) = -2cos(1π(-2x^2 - 5) - 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (3(-2((-1x + 2)/(2x + 2))^2 + 3((-1x + 2)/(2x + 2)) + 2) - 1)/(-1(-2((-1x + 2)/(2x + 2))^2 + 3((-1x + 2)/(2x + 2)) + 2)) and g(x) = -1|((-2x - 1)/(-3x - 2)) - 2| - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-1(-5(3x^2 - 3x - 5)^2 - 2(3x^2 - 3x - 5) + 5) - 3)/(1(-5(3x^2 - 3x - 5)^2 - 2(3x^2 - 3x - 5) + 5) + 2) and g(x) = 2cos(1π((-2x)/(-2x + 3)) + 3) - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1e^(1((1(1x^2 + 1x - 1) - 3)/(3(1x^2 + 1x - 1) + 1))) + 1 and g(x) = -1(1|x - 1| + 1)^2 + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1|((-1(-4x - 4) + 3)/(1(-4x - 4) - 3))| - 3 and g(x) = 2cos(3π(-2x + 5) + 3) - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3(1(3x + 2) - 4)^2 + 4(1(3x + 2) - 4) + 2 = -2((-1x - 3)/(2x + 3))^2 - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1|((3(-1x - 5) - 3)/(3(-1x - 5) - 2)) + 3| + 2 and g(x) = -1(-2|x| + 2)^2 - 3(-2|x| + 2) - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3cos(2π((2((1x - 3)/(1x - 2)) - 2)/(-2((1x - 3)/(1x - 2)) - 1)) + 3) + 3 and g(x) = -3(-2cos(3πx + 2) - 1) - 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -4(-1((1x - 3)/(1x + 1)) + 4)^2 + 4(-1((1x - 3)/(1x + 1)) + 4) + 3 and g(x) = -1|((-3x - 2)/(-2x + 1)) + 3| intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1((-2(3sin(1πx - 3) - 3) - 1)/(-1(3sin(1πx - 3) - 3) + 2)) + 4 and g(x) = (-1(-1sin(2πx - 1)) - 2)/(-2(-1sin(2πx - 1)) - 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-3(1(-5x - 5)^2 - 2(-5x - 5) + 3) - 1)/(1(1(-5x - 5)^2 - 2(-5x - 5) + 3) + 3) and g(x) = 1(-1sin(1πx + 2) + 1)^2 + 3(-1sin(1πx + 2) + 1) - 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2cos(1π(-1|(3x^2 - 5x + 5) - 3| - 2) + 2) - 1 and g(x) = -1e^(1(-4x^2 + 5x - 2)) - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1(1(1|x + 2| - 2)^2 + 5(1|x + 2| - 2) + 3) + 5 and g(x) = -1sin(3π(2|x - 2| + 3) + 2) + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1(-1(-2x + 2)^2 - 5(-2x + 2) - 4) + 4 and g(x) = -1(2cos(1πx) + 2)^2 - 4(2cos(1πx) + 2) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1(4(1sin(2πx - 3) + 2)^2 - 4(1sin(2πx - 3) + 2) - 2) - 4 and g(x) = -2|(-5x^2 + 4x - 5) - 1| - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1(-3sin(2π(4x + 4) - 3) + 3)^2 + 1(-3sin(2π(4x + 4) - 3) + 3) - 1 = (2(-3|x + 2| - 3) - 3)/(-2(-3|x + 2| - 3) - 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3cos(1π(-5(1|x - 3| - 1) - 1) - 2) + 2 and g(x) = (-2(-1x^2 - 1x + 2) - 1)/(-2(-1x^2 - 1x + 2) - 1) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3(2sin(1π(3x^2 + 5x + 4) - 2) - 2)^2 - 1(2sin(1π(3x^2 + 5x + 4) - 2) - 2) - 2 = 5((1x + 1)/(-2x + 1))^2 + 4((1x + 1)/(-2x + 1)) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3((-1(-3e^(1x) + 3))/(-3(-3e^(1x) + 3) - 3)) - 5 and g(x) = -2sin(1π(3|x + 3| - 2) + 2) - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -4(-1cos(2π(-4x - 1) - 2)) and g(x) = 3(-3cos(3πx))^2 + 2(-3cos(3πx)) + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3|(-2|(3sin(3πx + 1) + 2) + 3| - 3) + 1| = 3(-2e^(-1x) - 2)^2 - 4(-2e^(-1x) - 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1(3sin(3π(-3x + 3) + 1)) + 1 and g(x) = (2(3|x - 1| + 3) - 1)/(-2(3|x - 1| + 3) - 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -4(2|(-3|x - 2| + 2)| - 1)^2 - 1(2|(-3|x - 2| + 2)| - 1) + 4 and g(x) = 1((-2x + 3)/(1x))^2 - 2((-2x + 3)/(1x)) - 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1(3(4x^2 - 2x)^2 - 1(4x^2 - 2x) - 2) - 3 and g(x) = -3(1sin(2πx + 3) - 1) - 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3(-1(-1sin(2πx - 3) + 2))^2 - 3(-1(-1sin(2πx - 3) + 2)) + 3 and g(x) = -1sin(3π((-1x + 2)/(-2x + 3)) + 2) - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(-2sin(1π((2x + 1)/(2x - 1)) + 1) + 3) + 1 = (3((-1x - 1)/(2x - 1)) + 1)/(1((-1x - 1)/(2x - 1))) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (2(-3sin(2π((-1x)/(-2x + 3))) + 3) - 3)/(-2(-3sin(2π((-1x)/(-2x + 3))) + 3)) and g(x) = 1cos(1π((1x + 3)/(2x - 3)) + 3) + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-1(-5(2cos(1πx - 1) - 3)^2 + 5(2cos(1πx - 1) - 3) - 1) - 3)/(2(-5(2cos(1πx - 1) - 3)^2 + 5(2cos(1πx - 1) - 3) - 1) + 1) and g(x) = 2sin(1π(-4x^2 - 2x - 4) + 2) - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1(-4(-3cos(2πx - 3))^2 + 1(-3cos(2πx - 3)) + 5) + 3 and g(x) = 1|(-1|x - 3| + 2) - 2| - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2cos(2π(3((2x + 1)/(3x - 1)) + 4) + 1) - 1 and g(x) = -3|(-3cos(2πx + 2)) - 3| + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (2(2|(1x^2 - 1x - 4)| - 1))/(-2(2|(1x^2 - 1x - 4)| - 1) - 1) and g(x) = (-3(-4x^2 - 4x - 3))/(-3(-4x^2 - 4x - 3) - 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2|(-5((3x + 3)/(-3x + 2)) - 4) + 2| - 2 and g(x) = -2sin(2π(-1|x + 3| - 3) + 3) + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2cos(1π(1(4x^2 + 1x - 4)^2 - 2(4x^2 + 1x - 4) + 1)) + 2 and g(x) = (3((-2x + 1)/(1x + 2)) - 2)/(2((-2x + 1)/(1x + 2))) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (2(3cos(3π(-1|x + 1| + 3) - 3) + 1) + 3)/(3(3cos(3π(-1|x + 1| + 3) - 3) + 1) + 2) and g(x) = (3(3x^2 + 4x) - 3)/(-3(3x^2 + 4x) - 2) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3cos(2π((2((-1x - 1)/(2x + 2)) - 2)/(3((-1x - 1)/(2x + 2)) - 1)) + 3) - 2 and g(x) = 1cos(3π(-1|x + 2| - 3) + 1) - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (3(-1(2|x| + 1)^2 + 1(2|x| + 1) + 1) + 1)/(-1(-1(2|x| + 1)^2 + 1(2|x| + 1) + 1) - 2) and g(x) = -2cos(2π(-1x^2 + 3x - 1) + 2) + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-2(-2|(-2|x - 1| - 2) - 1| - 3) - 2)/(2(-2|(-2|x - 1| - 2) - 1| - 3) + 2) and g(x) = 3e^(-1(1x^2 + 1x + 4)) - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -4((-1(-3sin(1πx) + 1) - 3)/(-1(-3sin(1πx) + 1) - 1)) + 1 and g(x) = (-3(-2|x| - 3) + 3)/(1(-2|x| - 3) + 3) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3|(-2|(5x + 1)|) - 1| + 2 and g(x) = 2(2cos(2πx - 1) + 2)^2 + 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3sin(3π(3|(1x + 3)| - 2) - 3) - 2 = (3((1x - 1)/(1x + 2)))/(-2((1x - 1)/(1x + 2)) + 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1cos(2π(-5(1|x - 1|)^2 + 1(1|x - 1|) + 5) + 1) + 2 and g(x) = 2e^(-1(4x + 1)) + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2(-1(-1|x - 3|) - 4)^2 - 2(-1(-1|x - 3|) - 4) + 4 = 3(-1cos(1πx + 2))^2 + 3(-1cos(1πx + 2)) + 5 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1((2(3sin(1πx + 2) + 2) - 1)/(-2(3sin(1πx + 2) + 2) + 3))^2 - 4((2(3sin(1πx + 2) + 2) - 1)/(-2(3sin(1πx + 2) + 2) + 3)) + 5 = 2|(3|x - 3| + 2) + 1| have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (3(2(-2sin(2πx + 1) - 1)^2 - 4(-2sin(2πx + 1) - 1) - 5))/(-2(2(-2sin(2πx + 1) - 1)^2 - 4(-2sin(2πx + 1) - 1) - 5) + 1) and g(x) = 3sin(3π(-3x) + 2) + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2|(1cos(3π((-1x - 3)/(-2x)) + 2)) + 3| - 1 and g(x) = 5(2|x - 1| - 3) - 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (2(-4((1x - 3)/(2x - 1))^2 + 3((1x - 3)/(2x - 1)) - 2) + 2)/(1(-4((1x - 3)/(2x - 1))^2 + 3((1x - 3)/(2x - 1)) - 2) - 2) = -1cos(2π((2x + 2)/(1x))) + 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (2(-2sin(3π(5x^2 + 3x - 4) - 1) + 2) - 1)/(3(-2sin(3π(5x^2 + 3x - 4) - 1) + 2) - 2) = 1(4x^2 - 2x - 3) - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -5((3(2|x + 2| - 2) + 3)/(-2(2|x + 2| - 2) - 3))^2 + 1((3(2|x + 2| - 2) + 3)/(-2(2|x + 2| - 2) - 3)) and g(x) = -3cos(1π(1x^2 + 4x + 2)) + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1|(-4(1|x - 1| - 2)^2 + 4(1|x - 1| - 2) - 3)| + 3 and g(x) = (1(-1x^2 - 5x + 2) + 3)/(2(-1x^2 - 5x + 2) + 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3e^(-1((-2(1x + 5))/(-2(1x + 5) - 3))) - 1 and g(x) = -2sin(2π(2x - 2) - 1) - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -5((-1((2x + 1)/(-3x + 1)) + 2)/(1((2x + 1)/(-3x + 1)) - 3))^2 - 5((-1((2x + 1)/(-3x + 1)) + 2)/(1((2x + 1)/(-3x + 1)) - 3)) - 5 = 2sin(1π(-2x^2 - 5x + 5) + 2) - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1cos(3π(1|(-4x^2 - 2x + 5) + 2| - 3) + 2) + 1 and g(x) = -1e^(-1(2x^2 + 2x - 3)) + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 4(-1|((-2x + 1)/(2x + 2))| + 1)^2 - 4(-1|((-2x + 1)/(2x + 2))| + 1) and g(x) = -1(-1sin(3πx + 3)) + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -5((-2(2cos(3πx - 3) + 1) + 2)/(2(2cos(3πx - 3) + 1) + 1))^2 + 3((-2(2cos(3πx - 3) + 1) + 2)/(2(2cos(3πx - 3) + 1) + 1)) - 2 and g(x) = -3e^(2(1x^2 + 1)) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3|(2e^(2(-2|x| + 1)) + 2) - 3| + 2 = 2cos(3π(-2x + 5) - 3) - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3(3cos(2π(4x^2 + 2x - 1) - 3) + 2) - 1 and g(x) = (2(-4x - 4))/(3(-4x - 4) + 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2(-2(3|x - 1|) - 1) + 1 and g(x) = 1(4x^2 - 1x - 4)^2 - 3(4x^2 - 1x - 4) + 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3((2((2x - 1)/(-2x - 1)) + 3)/(-3((2x - 1)/(-2x - 1)) + 4)) - 1 and g(x) = 1cos(3π(4x - 3) - 1) + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1cos(2π(3((1x - 2)/(-2x + 3)) + 1) + 2) + 3 and g(x) = 2sin(1π(-1x + 4) - 2) + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1|(-3sin(3π((3x - 2)/(3x + 1)) - 2) + 2) + 2| - 1 and g(x) = (2(2|x - 1| - 3))/(-3(2|x - 1| - 3) + 2) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-2(-3sin(2π((-1x - 1)/(-1x + 3)) - 2)) + 1)/(-2(-3sin(2π((-1x - 1)/(-1x + 3)) - 2)) - 2) and g(x) = 2|(5x + 5) - 2| intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (1(-1sin(3π((2x + 3)/(2x - 3)) + 3) - 1))/(-2(-1sin(3π((2x + 3)/(2x - 3)) + 3) - 1) - 1) and g(x) = 3(-2|x + 1| - 2) + 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2e^(1(-3(5x^2 + 4x - 1) - 2)) and g(x) = 3sin(3π(-3x + 2) - 2) + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3cos(3π((-2(5x + 2) - 3)/(-2(5x + 2))) - 3) and g(x) = -1cos(1π(1x + 3) - 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1(2sin(2π((-1x + 1)/(-2x - 3)) - 2) - 2)^2 - 5(2sin(2π((-1x + 1)/(-2x - 3)) - 2) - 2) = (2(1cos(3πx + 1) + 2) - 2)/(3(1cos(3πx + 1) + 2) - 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3|(-1e^(-1(-2|x + 3| - 1)) + 3) + 3| + 3 and g(x) = (1(1|x - 2| - 3) - 2)/(2(1|x - 2| - 3) + 2) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (1(1((-3x)/(-2x - 2))^2 + 5((-3x)/(-2x - 2)) + 1) + 1)/(-3(1((-3x)/(-2x - 2))^2 + 5((-3x)/(-2x - 2)) + 1) - 1) and g(x) = -3sin(3π(3|x| - 1) - 3) + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3sin(2π(-2|(1x^2 - 2x + 3) + 2| - 1) - 2) - 2 and g(x) = (-3(-1x^2 + 4x) + 2)/(1(-1x^2 + 4x) + 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -4((1((1x - 3)/(-3x - 3)))/(1((1x - 3)/(-3x - 3)) + 1))^2 + 4((1((1x - 3)/(-3x - 3)))/(1((1x - 3)/(-3x - 3)) + 1)) + 3 and g(x) = 1sin(1π(-4x^2 + 1x + 2)) + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(2(4x - 4) + 4)^2 - 4 = 1cos(1π((3x + 3)/(-3x + 1)) + 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (3(3sin(3π(-3|x| + 2) + 2) + 1))/(2(3sin(3π(-3|x| + 2) + 2) + 1) + 2) and g(x) = -3sin(3π(-3|x - 1|) + 3) - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1(-2(2x^2 + 1x - 3)^2 - 3(2x^2 + 1x - 3))^2 - 4(-2(2x^2 + 1x - 3)^2 - 3(2x^2 + 1x - 3)) + 5 and g(x) = -3|(2sin(1πx - 1) + 3) - 1| - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1|(1(-4x + 4)^2 - 4(-4x + 4) - 1) - 3| + 1 = 1(-3sin(3πx + 1) - 3) + 5 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1(-2cos(3π(-4x) + 3) + 1)^2 - 1(-2cos(3π(-4x) + 3) + 1) and g(x) = -2(1x + 1)^2 + 5(1x + 1) + 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-1(-2|(-3|x - 1| + 1) - 2| - 2) - 3)/(3(-2|(-3|x - 1| + 1) - 2| - 2) + 2) and g(x) = 2cos(2π((1x - 1)/(-1x + 2)) + 2) - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2(-1(4x^2 + 1x - 3) + 1)^2 - 4(-1(4x^2 + 1x - 3) + 1) - 4 = -2(-3x - 5) - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 4(-2cos(3π(-3x^2 + 2x + 3) - 2) + 2)^2 - 5(-2cos(3π(-3x^2 + 2x + 3) - 2) + 2) - 3 and g(x) = 3(-2|x + 1| - 1) + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-3(5((-1x)/(-1x + 2)) - 4))/(-3(5((-1x)/(-1x + 2)) - 4) + 2) and g(x) = 3(1|x - 2| - 3)^2 - 3(1|x - 2| - 3) - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -4(2|(-1|x + 2|) + 3|)^2 - 2(2|(-1|x + 2|) + 3|) - 2 and g(x) = 1cos(3π(1|x + 2|)) - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2|(2|(-1e^(1x) + 2) + 2| - 1) - 1| + 3 and g(x) = 2(-2sin(1πx + 3))^2 + 2(-2sin(1πx + 3)) + 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3|(1((-2x + 1)/(-1x - 1))^2 - 5) + 2| + 2 and g(x) = 1sin(3π(1|x - 2| + 3) + 1) - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1sin(3π(1|((-1x + 1)/(-2x - 3)) - 1| + 1) - 2) - 3 and g(x) = -2e^(-1(-3x - 5)) + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3((1(-2e^(-2x) - 3) + 3)/(2(-2e^(-2x) - 3) - 1)) and g(x) = -1|(2|x + 2| - 3) + 2| + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (1(-2e^(-2(1x^2 - 1x - 2)) - 3) + 1)/(3(-2e^(-2(1x^2 - 1x - 2)) - 3) - 1) and g(x) = 1cos(2π(2x^2 - 4x + 1) - 1) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -5((-2(-1|x - 2| + 2) - 2)/(-1(-1|x - 2| + 2) - 3)) - 4 = -2sin(3π(5x^2 + 3x + 3) - 3) + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2e^(1(-1|(-2|x + 2| + 1) + 1| - 3)) + 1 and g(x) = 2cos(2π(2|x| + 1) + 1) - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2(1|(-1x - 1) + 3| - 1)^2 + 2(1|(-1x - 1) + 3| - 1) + 5 and g(x) = 3cos(1π(1x^2 - 5x + 3) - 2) + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -4(-3sin(1π(-3x^2 - 3x - 3) + 1) + 1)^2 + 1(-3sin(1π(-3x^2 - 3x - 3) + 1) + 1) + 4 and g(x) = 3|(3sin(3πx + 3) - 2) + 2| + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2(1sin(3π(-5x^2 - 1x + 3) + 2) + 1) - 1 and g(x) = 4(-2|x - 2| - 1)^2 + 5(-2|x - 2| - 1) + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2|(-2(3cos(3πx - 3) + 3)^2 + 4(3cos(3πx - 3) + 3) + 5) + 3| + 3 and g(x) = -1e^(-1(-2|x - 3| - 1)) - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (1(-1(-4x^2 - 3x + 4)^2 - 1(-4x^2 - 3x + 4) + 3) + 2)/(3(-1(-4x^2 - 3x + 4)^2 - 1(-4x^2 - 3x + 4) + 3) + 2) and g(x) = (-2(2e^(1x) - 2) + 2)/(-2(2e^(1x) - 2) + 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-1(-1|(2sin(2πx + 3) - 1) - 2| + 2) + 2)/(-1(-1|(2sin(2πx + 3) - 1) - 2| + 2) + 3) and g(x) = (-1(-2|x| + 1) - 1)/(-1(-2|x| + 1) + 3) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2|(3cos(3π(1|x| + 2) + 1)) + 2| + 3 and g(x) = (-3(5x) - 2)/(-2(5x) - 1) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2cos(2π(4(-3x - 3) - 4) + 1) - 3 and g(x) = 3cos(2π(-1|x - 2| + 2) - 1) - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3|(-5(2sin(1πx) + 1)^2 + 3(2sin(1πx) + 1) + 3)| + 3 and g(x) = 1(4x^2 + 4x - 4) - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3sin(2π(2|(-1x^2 - 1x + 4) + 2| - 3) - 1) - 3 and g(x) = -3e^(1(1|x + 3| - 1)) - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 5((-2(2cos(3πx - 3) - 3) - 3)/(2(2cos(3πx - 3) - 3) + 1))^2 + 4((-2(2cos(3πx - 3) - 3) - 3)/(2(2cos(3πx - 3) - 3) + 1)) - 4 and g(x) = -1|(-2|x + 1| - 2) - 1| - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (3((-2(-1sin(2πx + 1) + 2) - 1)/(3(-1sin(2πx + 1) + 2) + 1)) - 1)/(-1((-2(-1sin(2πx + 1) + 2) - 1)/(3(-1sin(2πx + 1) + 2) + 1)) - 1) and g(x) = -5(-2cos(1πx - 3) - 2) + 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1(5(-3|x + 2| + 3)^2 + 1(-3|x + 2| + 3) - 5)^2 - 3(5(-3|x + 2| + 3)^2 + 1(-3|x + 2| + 3) - 5) - 4 and g(x) = 1sin(1π((-3x - 1)/(2x + 1)) - 3) - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2|((1(-5x - 1) - 2)/(2(-5x - 1) - 3))| = -2cos(3π(-2|x + 1| - 1) - 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 5(-1|(1sin(3πx + 1)) + 1| + 1) - 1 and g(x) = 3(-2sin(2πx)) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2|((-1(-4x + 2) + 2)/(-1(-4x + 2) - 2)) - 2| = -5(2e^(1x) - 2)^2 + 1(2e^(1x) - 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1|(-2(2cos(1πx + 1) + 1) + 1)| = -2e^(-2(1|x + 3| - 1)) + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2cos(2π((-3(-3x^2 + 4x + 2) + 3)/(-3(-3x^2 + 4x + 2) + 2)) + 1) - 2 and g(x) = -3(-2cos(3πx + 3) - 1) - 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1sin(3π(3(-5x^2 - 2x - 1) + 4) - 3) - 1 and g(x) = -3((3x - 2)/(-3x)) - 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(-3|((3x + 3)/(-3x + 4)) - 1| + 2)^2 + 2(-3|((3x + 3)/(-3x + 4)) - 1| + 2) - 5 = -5(1e^(-1x) - 1)^2 + 5(1e^(-1x) - 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-2(3sin(2π(1x^2 - 5x + 2) - 1) + 3) + 2)/(1(3sin(2π(1x^2 - 5x + 2) - 1) + 3) + 3) and g(x) = -2(2|x - 1| - 1)^2 + 1(2|x - 1| - 1) + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3((2(-2sin(3πx - 1) + 1) - 3)/(3(-2sin(3πx - 1) + 1)))^2 - 5((2(-2sin(3πx - 1) + 1) - 3)/(3(-2sin(3πx - 1) + 1))) + 2 and g(x) = 1(2|x - 1| - 1) - 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(-3|(-2sin(1πx - 3) + 1)| + 3)^2 + 2(-3|(-2sin(1πx - 3) + 1)| + 3) - 3 = 3|(2x^2 + 4x - 2) - 2| + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2|(4(-1sin(3πx) + 2) - 5) + 2| + 1 and g(x) = (-2(-4x - 2) - 1)/(1(-4x - 2)) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3(-2(1cos(2πx + 2) + 3)^2 + 1(1cos(2πx + 2) + 3))^2 + 1(-2(1cos(2πx + 2) + 3)^2 + 1(1cos(2πx + 2) + 3)) + 4 and g(x) = 3(4x^2 + 4x + 2)^2 - 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (3(-1((2x - 2)/(-2x + 3)) - 3) + 1)/(3(-1((2x - 2)/(-2x + 3)) - 3) - 2) and g(x) = 1|(-1sin(3πx - 3)) + 2| - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3|((-2(-1|x - 2| + 1) - 2)/(2(-1|x - 2| + 1) - 1)) + 3| + 1 and g(x) = 2((-2x - 1)/(1x))^2 + 1((-2x - 1)/(1x)) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 4(-3sin(2π(-2x^2 - 1x - 1))) + 1 = 1e^(-2((-1x + 2)/(-2x + 3))) + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1(-3(-2sin(2πx - 3) - 1)^2 - 3(-2sin(2πx - 3) - 1) + 2)^2 - 5(-3(-2sin(2πx - 3) - 1)^2 - 3(-2sin(2πx - 3) - 1) + 2) - 1 and g(x) = (1(-2|x - 3| - 2) + 2)/(-1(-2|x - 3| - 2) + 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2|(2((-3x + 2)/(-2x - 1))^2 + 5((-3x + 2)/(-2x - 1)) - 1) + 3| + 1 and g(x) = -2sin(2π(-1x^2 + 5x + 4)) - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1(3sin(2π(1|x + 2| - 2) + 1))^2 + 4(3sin(2π(1|x + 2| - 2) + 1)) - 2 and g(x) = -3cos(3π(-4x^2 - 2x + 3) - 3) + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}