messages listlengths 1 1 | ground_truth stringclasses 186 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "How many zeros does the function f(x) = -1((1(2|(3x)| + 2) - 1)/(-1(2|(3x)| + 2) + 2))^2 + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (3(-3sin(3πx - 3) + 1) + 2)/(-2(-3sin(3πx - 3) + 1) - 2) 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) = 1(1((-2(-1|x + 1| - 2) - 1)/(1(-1|x + 1| - 2) + 3)) + 5)^2 + 2(1((-2(-1|x + 1| - 2) - 1)/(1(-1|x + 1| - 2) + 3)) + 5) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation 5(2cos(2π(3|(4x^2 + 1x - 3) - 3| - 3) - 3) - 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 799 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2π(-1(-1|(-1x + 5) + 2| - 1)^2 - 1(-1|(-1x + 5) + 2| - 1) + 2) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 636 | MATH |
[
{
"content": "How many solutions does the equation 2(2((2x)/(1x + 1))^2 - 4((2x)/(1x + 1)) - 3) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many solutions does the equation -1e^(2(-3((-1(-4x^2 + 3x + 2))/(3(-4x^2 + 3x + 2) + 3)) - 2)) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(2π((2(-3|x - 2| - 2) - 3)/(-1(-3|x - 2| - 2) + 3))) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2|((2(-2(-2x^2 - 1x - 5) - 2) - 2)/(1(-2(-2x^2 - 1x - 5) - 2) + 3)) - 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -4(2|(1((-1x - 3)/(3x - 2))^2 - 4((-1x - 3)/(3x - 2)) - 3) - 1| - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3cos(3π(-2|((2(-5x^2 + 5) - 3)/(-1(-5x^2 + 5) + 2)) - 1| + 3) - 2) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 64 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (2(3(-1|x - 1| + 1)^2 + 3(-1|x - 1| + 1)) + 1)/(1(3(-1|x - 1| + 1)^2 + 3(-1|x - 1| + 1)) + 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(-3sin(1πx + 1) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(3cos(1π(-4x^2 + 2x - 3) + 1) - 3) - 2)/(2(3cos(1π(-4x^2 + 2x - 3) + 1) - 3) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 497 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3(3|x + 3|) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3(-2|(3x^2 - 1x - 1)| + 1) + 2 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 (-3(2cos(3π(-3|(1x^2 - 3x - 2) - 2|) - 3) + 1) - 1)/(-1(2cos(3π(-3|(1x^2 - 3x - 2) - 2|) - 3) + 1) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1177 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-3|(2cos(1πx + 1) - 3) + 3| + 3) - 1)/(1(-3|(2cos(1πx + 1) - 3) + 3| + 3) - 3) equals zero.\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) = -1|(1(-2((3x - 3)/(-2x + 3))^2 + 4((3x - 3)/(-2x + 3)) + 3) - 2) - 2| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(1|(1((3x + 1)/(1x + 1)) + 1) - 1| + 1)^2 - 2(1|(1((3x + 1)/(1x + 1)) + 1) - 1| + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many solutions does the equation -1cos(2π(-1x - 2)) + 1 = 0 have in the range [-10, 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) = (-1(2(2(-2|x - 3| + 2)^2 + 1(-2|x - 3| + 2)) - 5))/(-2(2(2(-2|x - 3| + 2)^2 + 1(-2|x - 3| + 2)) - 5) + 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) = 3cos(1π(-3|(4x^2 + 2x - 1) + 2| - 2) + 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 971 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-2sin(1π(1|x| - 1) - 2) + 1)^2 - 2(-2sin(1π(1|x| - 1) - 2) + 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many zeros does the function f(x) = 5(-3((-2x - 3)/(1x + 3))^2 + 1((-2x - 3)/(1x + 3)) + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3(1|(-2x + 1) + 3|)^2 + 4(1|(-2x + 1) + 3|) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -5(-4((3(1e^(2x) - 1) - 2)/(-3(1e^(2x) - 1) + 4)))^2 + 3(-4((3(1e^(2x) - 1) - 2)/(-3(1e^(2x) - 1) + 4))) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(3π(-2x^2 - 2x - 4) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1168 | MATH |
[
{
"content": "How many solutions does the equation 1(3(-1|((2x + 2)/(-3x - 2)) - 2| + 1))^2 - 5 = 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) = -3(-1|(-1e^(-1x) + 2) + 3| + 2)^2 + 3(-1|(-1e^(-1x) + 2) + 3| + 2) + 1 where -10 ≤ x ≤ 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(2(5(-1|x| + 3)^2 + 5(-1|x| + 3)) - 1) + 1)/(1(2(5(-1|x| + 3)^2 + 5(-1|x| + 3)) - 1)) 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 5(-2|((2(-4x - 3) + 2)/(-2(-4x - 3) - 1)) - 2| - 1)^2 + 5(-2|((2(-4x - 3) + 2)/(-2(-4x - 3) - 1)) - 2| - 1) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3sin(3π(-4x^2 - 1x - 2) + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1338 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1|((-2(-2(-3sin(3πx + 3) - 1)^2 + 5(-3sin(3πx + 3) - 1) - 1) + 2)/(2(-2(-3sin(3πx + 3) - 1)^2 + 5(-3sin(3πx + 3) - 1) - 1) + 2)) - 3| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 146 | MATH |
[
{
"content": "How many solutions does the equation 5((-1(-3|(1x + 3) - 1| + 3) - 2)/(2(-3|(1x + 3) - 1| + 3) + 2))^2 - 1((-1(-3|(1x + 3) - 1| + 3) - 2)/(2(-3|(1x + 3) - 1| + 3) + 2)) - 4 = 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(3|(-3x^2 - 3x + 4) - 2| - 2) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1613 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(1π(-5x^2 + 2x - 3) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1000 | MATH |
[
{
"content": "How many solutions does the equation 5(-3sin(3πx) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2(-3(-2|x - 1|)^2 + 2(-2|x - 1|) + 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many solutions does the equation (-2(-1|(5(-2x^2 + 1x + 3) + 4) - 1| + 2) - 2)/(-2(-1|(5(-2x^2 + 1x + 3) + 4) - 1| + 2) - 3) = 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) = (3(1cos(1π(1(-3|x - 3| + 1)^2 - 1(-3|x - 3| + 1) + 1) + 3)))/(-1(1cos(1π(1(-3|x - 3| + 1)^2 - 1(-3|x - 3| + 1) + 1) + 3)) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1412 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(3cos(3π(5(2|x| - 3)^2 + 2(2|x| - 3) - 5) - 1) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1041 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-3sin(2πx + 3))^2 - 2(-3sin(2πx + 3)) - 3 equals zero.\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(-2cos(3πx - 1) + 2) - 2) + 3)/(3(1(-2cos(3πx - 1) + 2) - 2) + 1) where -10 ≤ x ≤ 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) = -4(2|(3x^2 - 3x + 2) - 1| - 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1(-3x^2 + 3x + 3) + 2)/(2(-3x^2 + 3x + 3) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many solutions does the equation 3((3(-1x + 2) + 1)/(2(-1x + 2)))^2 + 4((3(-1x + 2) + 1)/(2(-1x + 2))) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many zeros does the function f(x) = 5(-3((-1x + 1)/(3x))^2 - 5((-1x + 1)/(3x)) + 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -4((-1(2(2|x - 3| - 1) + 3) + 3)/(1(2(2|x - 3| - 1) + 3) - 2))^2 - 5((-1(2(2|x - 3| - 1) + 3) + 3)/(1(2(2|x - 3| - 1) + 3) - 2)) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1|(-2e^(-2(1(2x^2 + 4x - 2) - 5)) + 2) + 3| + 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) = -1((-2(1(1|x| - 2)^2 - 3(1|x| - 2) - 2) + 3)/(-1(1(1|x| - 2)^2 - 3(1|x| - 2) - 2))) - 5 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) = -2sin(3π((1(-5x^2 - 5x - 2) + 1)/(1(-5x^2 - 5x - 2) - 3))) + 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) = -3(-1|x| + 1)^2 + 3(-1|x| + 1) + 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many solutions does the equation -2cos(3π((-2x - 2)/(-1x + 2)) + 2) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 143 | MATH |
[
{
"content": "How many zeros does the function f(x) = 5(-1x^2 - 5x + 5) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(2((-3x - 1)/(1x)) - 1) + 1| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-1(3cos(1π(-1|x + 2| - 3) - 1) + 1))/(-2(3cos(1π(-1|x + 2| - 3) - 1) + 1) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2cos(1π(1((-2(-4x^2 - 5x - 4))/(-1(-4x^2 - 5x - 4) - 3)) - 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 86 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1cos(2π((2(-3x - 4) - 2)/(-1(-3x - 4) - 3)) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 88 | MATH |
[
{
"content": "How many solutions does the equation (1(-1cos(3π(3x - 3) + 2) + 3) - 2)/(1(-1cos(3π(3x - 3) + 2) + 3)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(1π(1|x - 1| - 1) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3|((2(-1(-1x + 4)^2 - 5(-1x + 4) + 4) + 3)/(-3(-1(-1x + 4)^2 - 5(-1x + 4) + 4) + 2))| + 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) = 4(3|(4x^2 - 1x - 5) + 3| - 3) + 5 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|(-1cos(2πx - 2) - 3) + 1| + 3 have in the interval [-10, 10]?\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) = -4(2|(-1x^2 - 2x + 3) + 2| - 2) + 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(-1x - 5)^2 + 5(-1x - 5) + 2) + 1)/(2(3(-1x - 5)^2 + 5(-1x - 5) + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many solutions does the equation 3|(4(1sin(3πx + 1) - 1)) + 2| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3|(-5(2((-3x + 2)/(3x + 1))^2 + 4((-3x + 2)/(3x + 1))) + 1) - 3| + 2 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 2sin(3π(-3|((-2x - 1)/(-3x + 4)) - 1| - 3) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 118 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1|((-3(2(-5x - 1)^2 - 5))/(3(2(-5x - 1)^2 - 5) - 2)) + 2| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation (-1(3(3cos(3πx + 3) + 1)^2 + 4(3cos(3πx + 3) + 1) + 3) + 3)/(-1(3(3cos(3πx + 3) + 1)^2 + 4(3cos(3πx + 3) + 1) + 3) - 1) = 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 2|((-2(-4(1x^2 + 4x) + 2) + 2)/(-2(-4(1x^2 + 4x) + 2) - 3)) - 1| - 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) = 2(-2|(5((-2x - 2)/(-1x - 2))^2 + 5((-2x - 2)/(-1x - 2)) - 5) - 1| + 1) + 5 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) = 1|((-1(4(-1x^2 + 5x + 2) - 1) - 2)/(-3(4(-1x^2 + 5x + 2) - 1) + 2)) - 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 solutions does the equation (-2(-2(-1|x + 2| + 3)^2 + 2) - 2)/(-2(-2(-1|x + 2| + 3)^2 + 2) + 1) = 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) = 1(1x - 1)^2 - 4(1x - 1) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(2|((-2(-5x - 3) + 2)/(-3(-5x - 3) + 4)) - 1| - 3)^2 - 2(2|((-2(-5x - 3) + 2)/(-3(-5x - 3) + 4)) - 1| - 3) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3cos(1π(-4x^2 + 5) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 800 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1e^(2((-2(-4(-1x - 5)^2 + 1(-1x - 5) + 2) + 1)/(3(-4(-1x - 5)^2 + 1(-1x - 5) + 2) - 1))) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1cos(2π(-2(3(1|x - 3| + 2) + 5)^2 - 1(3(1|x - 3| + 2) + 5) + 5)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1182 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -5(5x + 4)^2 + 5(5x + 4) + 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-3(-4(-3sin(3πx) + 2) + 3))/(-1(-4(-3sin(3πx) + 2) + 3) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many solutions does the equation -1((3(4(1|x - 3| - 3)^2 - 2) - 2)/(1(4(1|x - 3| - 3)^2 - 2) - 2)) + 4 = 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) = -1|(-1x - 4) - 2| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many solutions does the equation (-1(-1sin(1πx + 2) - 1) - 1)/(-2(-1sin(1πx + 2) - 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-1|(5x^2 - 4x + 2) - 3| + 3) - 2)/(1(-1|(5x^2 - 4x + 2) - 3| + 3) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many solutions does the equation 1(5(-3sin(2π(2|x - 3| + 1) - 1) + 1)^2 + 5(-3sin(2π(2|x - 3| + 1) - 1) + 1) - 2) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3((-2(2|x + 3| - 2) + 2)/(2(2|x + 3| - 2) + 3)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many solutions does the equation (1(-3cos(2π(-3|x| - 3) - 1) + 2) - 3)/(2(-3cos(2π(-3|x| - 3) - 1) + 2) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2|(3((2(5x^2 + 5x + 2) - 3)/(2(5x^2 + 5x + 2) + 2))) + 1| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1(4x - 3)^2 - 1(4x - 3) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many solutions does the equation -2(1((3x - 2)/(2x - 3))^2 - 1((3x - 2)/(2x - 3)) - 4) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many solutions does the equation (2(-3(-1(-1|x + 2| + 2)^2 - 3(-1|x + 2| + 2) + 5)) - 2)/(2(-3(-1(-1|x + 2| + 2)^2 - 3(-1|x + 2| + 2) + 5)) + 1) = 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) = -2sin(1π((-1x - 2)/(-2x + 3)) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(2(5(-2|x| + 1)^2 + 5(-2|x| + 1) - 2) - 5) + 1)/(-3(2(5(-2|x| + 1)^2 + 5(-2|x| + 1) - 2) - 5) + 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) = -1cos(3π(-3x - 4) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(3|(-2cos(1πx - 1) + 1) - 2|)^2 + 1(3|(-2cos(1πx - 1) + 1) - 2|) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1cos(2π(1|x - 3|) + 1) where -10 ≤ x ≤ 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) = -3(5((1x - 2)/(-2x + 1)) - 5)^2 - 3(5((1x - 2)/(-2x + 1)) - 5) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2cos(1π(1(-3x)^2 - 2(-3x) - 3) - 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1376 | MATH |
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