messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2((-2(1cos(3π(3x + 5)) - 3) - 2)/(-1(1cos(3π(3x + 5)) - 3) + 2)) + 2)/(2((-2(1cos(3π(3x + 5)) - 3) - 2)/(-1(1cos(3π(3x + 5)) - 3) + 2)) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 91 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1|(-1(-1(-2|x + 1| + 3)^2 - 2(-2|x + 1| + 3) + 3)^2 + 3(-1(-2|x + 1| + 3)^2 - 2(-2|x + 1| + 3) + 3) - 5) + 2| - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3(5(5((-1x - 3)/(-1x + 2)) + 2)^2 - 4(5((-1x - 3)/(-1x + 2)) + 2))^2 - 5(5(5((-1x - 3)/(-1x + 2)) + 2)^2 - 4(5((-1x - 3)/(-1x + 2)) + 2)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2|(-1cos(3π(-1((2x - 3)/(2x + 2))^2 + 1((2x - 3)/(2x + 2))) + 3) + 3) - 2| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 169 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3sin(3π((3(4((-2x - 1)/(-3x - 2))^2 - 2((-2x - 1)/(-3x - 2)) - 4) - 3)/(-3(4((-2x - 1)/(-3x - 2))^2 - 2((-2x - 1)/(-3x - 2)) - 4) + 2)) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 5 | MATH |
[
{
"content": "How many solutions does the equation (-1(3(-3sin(2π(-2|x + 3| + 2) - 1) + 2) - 2) + 2)/(-1(3(-3sin(2π(-2|x + 3| + 2) - 1) + 2) - 2)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(3cos(3π(-3(2x + 1) - 1) - 1) - 2))/(1(3cos(3π(-3(2x + 1) - 1) - 1) - 2) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 360 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3(4(-4((2x - 3)/(-1x - 3))^2 + 2) - 1)^2 - 2(4(-4((2x - 3)/(-1x - 3))^2 + 2) - 1) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 4(4(-3(1cos(2πx + 2) - 2)^2 + 5) - 2)^2 + 4(4(-3(1cos(2πx + 2) - 2)^2 + 5) - 2) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2(-1(-1|(-3x^2 + 2x + 5) - 1|) - 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2|((-3((-1(-1x^2 + 5x - 1) + 1)/(3(-1x^2 + 5x - 1) + 1)) + 1)/(-3((-1(-1x^2 + 5x - 1) + 1)/(3(-1x^2 + 5x - 1) + 1)) + 2)) - 2| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2sin(1π(2(-1(4x^2 - 5x - 5)^2 - 5(4x^2 - 5x - 5) - 1)^2 + 1(-1(4x^2 - 5x - 5)^2 - 5(4x^2 - 5x - 5) - 1) + 4) - 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 268 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3|(-1cos(1π(-5(-2|x + 1| + 3) - 4) - 1)) + 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2|(5(-3|((2x)/(2x + 3)) + 2| + 2) + 2) - 3| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = (3(-3(-4(-2|x - 1|)^2 - 5(-2|x - 1|) + 5)^2 + 4(-4(-2|x - 1|)^2 - 5(-2|x - 1|) + 5) + 5) - 3)/(1(-3(-4(-2|x - 1|)^2 - 5(-2|x - 1|) + 5)^2 + 4(-4(-2|x - 1|)^2 - 5(-2|x - 1|) + 5) + 5)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\b... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2cos(1π(2|(4(-2x^2 + 5)^2 + 2(-2x^2 + 5) - 2)| + 3) - 3) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1244 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3|(2sin(2π((3((-3x - 1)/(-3x + 1)) - 3)/(-3((-3x - 1)/(-3x + 1)) + 1)) + 1) + 1) + 1| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 49 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-3(1(-1cos(2π(-2|x - 1| + 1) + 3) - 3) + 4))/(-3(1(-1cos(2π(-2|x - 1| + 1) + 3) - 3) + 4) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many solutions does the equation 5(5((-1((1x - 3)/(2x)) + 1)/(1((1x - 3)/(2x)) + 1))^2 - 4((-1((1x - 3)/(2x)) + 1)/(1((1x - 3)/(2x)) + 1)) - 1)^2 - 1(5((-1((1x - 3)/(2x)) + 1)/(1((1x - 3)/(2x)) + 1))^2 - 4((-1((1x - 3)/(2x)) + 1)/(1((1x - 3)/(2x)) + 1)) - 1) - 1 = 0 have in the range [-10, 10]... | 4 | MATH |
[
{
"content": "How many solutions does the equation 1sin(3π((-2(-1(-1|x - 1| + 2)^2 - 1(-1|x - 1| + 2) + 1) - 2)/(-2(-1(-1|x - 1| + 2)^2 - 1(-1|x - 1| + 2) + 1) + 1)) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 123 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1|(-4(-2cos(3π(-2|x + 3| + 3) + 2) - 3) - 4) - 3| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "How many zeros does the function f(x) = -5((-2(-2cos(1π(-2|x - 1| - 2) - 1) + 3) + 3)/(-1(-2cos(1π(-2|x - 1| - 2) - 1) + 3) + 2))^2 + 3((-2(-2cos(1π(-2|x - 1| - 2) - 1) + 3) + 3)/(-1(-2cos(1π(-2|x - 1| - 2) - 1) + 3) + 2)) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: ... | 40 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(3π(5(2(-2|x + 3| - 1)^2 + 3(-2|x + 3| - 1) + 2)^2 + 1(2(-2|x + 3| - 1)^2 + 3(-2|x + 3| - 1) + 2) + 3)) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 530 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -5(3((-3(3x^2 - 3x - 5) - 2)/(2(3x^2 - 3x - 5) + 2))^2 - 1((-3(3x^2 - 3x - 5) - 2)/(2(3x^2 - 3x - 5) + 2)) - 5) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3cos(1π(1|(-3(-1|x| + 3)^2 + 1(-1|x| + 3) + 3) + 1| - 2) - 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 169 | MATH |
[
{
"content": "How many solutions does the equation -3sin(1π(-5(5(2x - 4)^2 - 3(2x - 4) - 5)^2 + 2(5(2x - 4)^2 - 3(2x - 4) - 5) - 3) - 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 341 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (1(2((2(-3cos(2πx + 3) - 1) - 2)/(2(-3cos(2πx + 3) - 1)))) - 1)/(-1(2((2(-3cos(2πx + 3) - 1) - 2)/(2(-3cos(2πx + 3) - 1)))) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1sin(3π((-3((-2(2|x + 1| + 1) + 2)/(2(2|x + 1| + 1))) + 2)/(2((-2(2|x + 1| + 1) + 2)/(2(2|x + 1| + 1))) + 2)) + 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 148 | MATH |
[
{
"content": "How many solutions does the equation -3(3(-3|(1x^2 - 5)| + 3)^2 - 2(-3|(1x^2 - 5)| + 3) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many solutions does the equation (1(1sin(3π(-4(-3|x| - 3) - 1)) - 3) + 3)/(2(1sin(3π(-4(-3|x| - 3) - 1)) - 3) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 718 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -4((-2((1(3cos(1πx + 3) - 2) - 2)/(1(3cos(1πx + 3) - 2) + 2)) - 3)/(2((1(3cos(1πx + 3) - 2) - 2)/(1(3cos(1πx + 3) - 2) + 2))))^2 + 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many solutions does the equation 3sin(3π(1|((2(2|x - 1| + 1) + 3)/(-1(2|x - 1| + 1) - 3)) - 3| - 3) - 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3cos(2π(4(-2|(1x - 4) - 1| - 2)^2 - 4(-2|(1x - 4) - 1| - 2) - 2) - 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1173 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3|(-1(-2|(3|x + 3| - 1) - 2| - 1)^2 - 5(-2|(3|x + 3| - 1) - 2| - 1) - 3) + 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2cos(1π(-2(4(-2|x + 1| - 2) + 3)^2 - 4(4(-2|x + 1| - 2) + 3)) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1453 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2|(2sin(3π(-1|(-2x + 3) + 1| - 2) - 1) - 1) - 1| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many solutions does the equation 2sin(2π(-3(2(1|x + 1| - 3) - 2)^2 - 4(2(1|x + 1| - 3) - 2) - 1) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 937 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-3(2sin(3π(4((-3x + 3)/(-1x + 3)) + 3) + 3) - 2))/(2(2sin(3π(4((-3x + 3)/(-1x + 3)) + 3) + 3) - 2) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 170 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(-5(-2(-3cos(1πx + 1) + 1)^2 + 4(-3cos(1πx + 1) + 1) - 1)^2 + 1(-2(-3cos(1πx + 1) + 1)^2 + 4(-3cos(1πx + 1) + 1) - 1))^2 + 3(-5(-2(-3cos(1πx + 1) + 1)^2 + 4(-3cos(1πx + 1) + 1) - 1)^2 + 1(-2(-3cos(1πx + 1) + 1)^2 + 4(-3cos(1πx + 1) + 1) - 1)) - 3 have in th... | 80 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(1π(-2(-3|(-1x - 3)|) - 3) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -5(-1(-2|(1e^(-2x) - 2) - 3| + 3)^2 + 3(-2|(1e^(-2x) - 2) - 3| + 3) + 4)^2 + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(-4(3sin(3π(-1|x - 2| + 2)) - 2) - 1) + 1| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many solutions does the equation 5((-3((3(-2cos(2πx + 3) - 1) - 1)/(3(-2cos(2πx + 3) - 1) + 3)) - 2)/(-1((3(-2cos(2πx + 3) - 1) - 1)/(3(-2cos(2πx + 3) - 1) + 3)) + 2)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2(-1cos(2π(-2(4x^2 + 3x - 5) + 1) + 2) + 2)^2 - 1(-1cos(2π(-2(4x^2 + 3x - 5) + 1) + 2) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1130 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(1cos(1π(-1(-2x^2 - 1x)^2 + 1(-2x^2 - 1x) + 3)) + 1)| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1302 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1|((-2(3(3|x - 2| + 1) - 3) - 2)/(-2(3(3|x - 2| + 1) - 3) + 3)) - 1| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2|(2|(4(-3x^2 + 3x) + 1) - 1| - 2) + 1| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (2(1(1|(1x^2 + 4x - 5)| - 2)^2 + 5(1|(1x^2 + 4x - 5)| - 2) - 4) - 3)/(2(1(1|(1x^2 + 4x - 5)| - 2)^2 + 5(1|(1x^2 + 4x - 5)| - 2) - 4)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation 4(1|((-2(3sin(1πx - 1) + 3) + 3)/(-1(3sin(1πx - 1) + 3))) + 2| - 2) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(2π((-2((-2(-4x + 5) - 1)/(1(-4x + 5))) + 1)/(1((-2(-4x + 5) - 1)/(1(-4x + 5))))) + 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2(-5(-3|(1x + 5)|)^2 + 1(-3|(1x + 5)|) + 2)^2 + 1(-5(-3|(1x + 5)|)^2 + 1(-3|(1x + 5)|) + 2) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1|(1(3cos(3π(1|x - 1| + 1) - 1) - 2) + 4) - 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 122 | MATH |
[
{
"content": "How many solutions does the equation 2sin(3π(1(5((1x + 2)/(2x - 1)) + 3) + 4) - 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 151 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(-5(1|(-3x^2 + 3) + 2|)^2 + 5(1|(-3x^2 + 3) + 2|) + 3) + 2)/(1(-5(1|(-3x^2 + 3) + 2|)^2 + 5(1|(-3x^2 + 3) + 2|) + 3) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(1π(3|(3|(3x - 3) - 2| - 1) + 1| - 1) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 540 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(2|((-1((1x + 1)/(-3x - 1)) - 1)/(-3((1x + 1)/(-3x - 1)) + 2)) + 1| - 2) - 3| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3(4(4(-2|x|)^2 + 3(-2|x|) - 4)^2 + 3(4(-2|x|)^2 + 3(-2|x|) - 4) + 2) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation -4(-2|(-3(4x - 1) + 3) + 1| + 1)^2 - 4(-2|(-3(4x - 1) + 3) + 1| + 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1(-1(2((2x - 2)/(-1x))^2 + 5((2x - 2)/(-1x)) + 2) + 5)^2 - 3(-1(2((2x - 2)/(-1x))^2 + 5((2x - 2)/(-1x)) + 2) + 5) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation (2(2cos(2π((-2(1|x - 1| + 1) + 2)/(-1(1|x - 1| + 1) - 3)) + 3) - 1) + 3)/(1(2cos(2π((-2(1|x - 1| + 1) + 2)/(-1(1|x - 1| + 1) - 3)) + 3) - 1) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 6 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3|(-2cos(3π((-2(4x - 3) - 2)/(-3(4x - 3) - 1)) + 1)) - 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2|(1|(-3sin(3π(1x + 5) + 3) + 3) + 1| - 3) + 1| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(2π(-5((-3(-4x^2 - 3x - 3) - 3)/(1(-4x^2 - 3x - 3) + 2))^2 + 2((-3(-4x^2 - 3x - 3) - 3)/(1(-4x^2 - 3x - 3) + 2)) - 3) + 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 179 | MATH |
[
{
"content": "How many solutions does the equation 2|(-1sin(1π(1(4x - 2) + 1) + 1) - 3) + 2| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many solutions does the equation -5(2sin(3π(3((-3x - 1)/(-3x + 4))^2 + 5((-3x - 1)/(-3x + 4)) + 1) - 2) - 1) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 148 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1(1|((-2(-5x^2 - 4x - 2) - 2)/(-1(-5x^2 - 4x - 2) - 2)) - 1| - 1) - 1)/(1(1|((-2(-5x^2 - 4x - 2) - 2)/(-1(-5x^2 - 4x - 2) - 2)) - 1| - 1) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 4 | MATH |
[
{
"content": "How many solutions does the equation -3sin(2π(1(4(1x + 2)^2 + 5(1x + 2) + 2)^2 - 1(4(1x + 2)^2 + 5(1x + 2) + 2) + 4)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 958 | MATH |
[
{
"content": "How many solutions does the equation -3cos(2π((2(-2|(1x^2 + 2x - 4) + 3|) - 2)/(-1(-2|(1x^2 + 2x - 4) + 3|) - 3)) - 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 231 | MATH |
[
{
"content": "How many zeros does the function f(x) = -5(-1|(2|(-1x + 1) + 3| - 1) - 2| + 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-2(3|(1x^2 + 5x - 4) - 3| - 2) + 1) - 3)/(-1(-2(3|(1x^2 + 5x - 4) - 3| - 2) + 1) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3(2(-5(-1x^2 + 4x + 1) - 1)^2 + 3(-5(-1x^2 + 4x + 1) - 1) - 1)^2 - 4(2(-5(-1x^2 + 4x + 1) - 1)^2 + 3(-5(-1x^2 + 4x + 1) - 1) - 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(2sin(3π((3(-4x + 4) + 2)/(-2(-4x + 4) - 1)) + 2) + 3) + 3)/(3(2sin(3π((3(-4x + 4) + 2)/(-2(-4x + 4) - 1)) + 2) + 3) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-3(3(-5(-3sin(2πx - 2) - 2)^2 - 1(-3sin(2πx - 2) - 2)) + 3))/(-1(3(-5(-3sin(2πx - 2) - 2)^2 - 1(-3sin(2πx - 2) - 2)) + 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1|((-3((3(1|x + 1| - 1) + 2)/(-3(1|x + 1| - 1) - 3)) + 1)/(-2((3(1|x + 1| - 1) + 2)/(-3(1|x + 1| - 1) - 3)) + 3)) - 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(4(-3(-2x^2 + 1x + 5)^2 - 4(-2x^2 + 1x + 5) + 3)^2 - 1(-3(-2x^2 + 1x + 5)^2 - 4(-2x^2 + 1x + 5) + 3)) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(3π((-2(4((3x - 2)/(-1x + 2)) - 1) - 3)/(-1(4((3x - 2)/(-1x + 2)) - 1))) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "How many solutions does the equation -1|(3(-1(4x^2 + 2x - 1) - 2)^2 + 4(-1(4x^2 + 2x - 1) - 2) - 5) + 2| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(3π(5(3((3x + 1)/(3x - 1)) + 3)^2 + 1(3((3x + 1)/(3x - 1)) + 3) - 5) - 3) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 374 | MATH |
[
{
"content": "How many solutions does the equation -1(-3cos(1π((-1(1|x + 1| - 1) + 3)/(3(1|x + 1| - 1) - 1)) + 2)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 65 | MATH |
[
{
"content": "How many solutions does the equation -1(1|(-2sin(2π((-3x)/(1x + 3)) + 2) + 1) - 3| - 2)^2 + 4(1|(-2sin(2π((-3x)/(1x + 3)) + 2) + 1) - 3| - 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 149 | MATH |
[
{
"content": "How many solutions does the equation 1cos(1π((1(1(3x - 4) + 2) + 1)/(-3(1(3x - 4) + 2) + 4)) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(3π(-2|(4(-2x + 5) - 4) - 1|) + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 464 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1cos(3π(1|(-3((-2x)/(-1x - 2)) - 3)| - 1) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 220 | MATH |
[
{
"content": "How many solutions does the equation -3sin(3π((-3(-2|((-3x + 1)/(-2x + 3)) - 3| + 2) - 1)/(-2(-2|((-3x + 1)/(-2x + 3)) - 3| + 2))) - 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 95 | MATH |
[
{
"content": "How many solutions does the equation 2sin(1π(4(3|(-1x^2 - 3x) - 1| + 2)^2 + 1(3|(-1x^2 - 3x) - 1| + 2) - 2) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1464 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(1|(4(1x^2 - 3x - 2)^2 - 3(1x^2 - 3x - 2) - 5) + 3| + 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3sin(1π(-1|(3|(-2|x| - 1) - 3| + 1) - 3| - 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1cos(1π((1(5(-3x^2 + 5) + 5) - 1)/(1(5(-3x^2 + 5) + 5) - 3)) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3|(-2|(1(1|x - 1| - 3)^2 + 5(1|x - 1| - 3) - 5) - 2| + 3) + 3| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2(-1(-2cos(3π(2|x + 2| + 2) + 3) - 1)^2 + 4(-2cos(3π(2|x + 2| + 2) + 3) - 1)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many solutions does the equation -2(-4(1(4x - 4) - 4)^2 + 3(1(4x - 4) - 4) + 1)^2 + 3(-4(1(4x - 4) - 4)^2 + 3(1(4x - 4) - 4) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2((-3(3|((1x - 2)/(-2x + 3))| - 2) - 3)/(-2(3|((1x - 2)/(-2x + 3))| - 2) + 1))^2 + 4((-3(3|((1x - 2)/(-2x + 3))| - 2) - 3)/(-2(3|((1x - 2)/(-2x + 3))| - 2) + 1)) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 4 | MATH |
[
{
"content": "How many solutions does the equation -2((-3(-2sin(3π(2|x + 3| + 2) + 2) + 2) - 2)/(-3(-2sin(3π(2|x + 3| + 2) + 2) + 2) + 2)) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many solutions does the equation (3(-1(4(3cos(3πx) + 2) + 5)^2 + 2(4(3cos(3πx) + 2) + 5)))/(1(-1(4(3cos(3πx) + 2) + 5)^2 + 2(4(3cos(3πx) + 2) + 5)) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3|(3((2(1cos(2πx + 3) - 1) + 2)/(1(1cos(2πx + 3) - 1) + 3)) + 1) + 3| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-3(2(3cos(3π(2|x + 1| - 1) + 2) + 2) - 5))/(-2(2(3cos(3π(2|x + 1| - 1) + 2) + 2) - 5) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many solutions does the equation (-1(1(-1e^(2(-2x^2 + 2x + 2)))^2 + 5(-1e^(2(-2x^2 + 2x + 2)))) - 2)/(-2(1(-1e^(2(-2x^2 + 2x + 2)))^2 + 5(-1e^(2(-2x^2 + 2x + 2)))) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1e^(-2(-1|(-4(-3x^2 + 2x + 3) - 5) + 1| + 2)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3(3(3(-3|x + 1| + 2) - 2) + 5)^2 + 5(3(3(-3|x + 1| + 2) - 2) + 5) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2sin(3π(4((-2(4x^2 - 1x - 1) - 1)/(1(4x^2 - 1x - 1) + 2))^2 - 3((-2(4x^2 - 1x - 1) - 1)/(1(4x^2 - 1x - 1) + 2)) + 5) + 3) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 65 | MATH |
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