messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "How many zeros does the function f(x) = -2(-2sin(1π(3((-2x + 2)/(-3x + 2))^2 - 4((-2x + 2)/(-3x + 2)) + 4) - 3) - 2)^2 + 3(-2sin(1π(3((-2x + 2)/(-3x + 2))^2 - 4((-2x + 2)/(-3x + 2)) + 4) - 3) - 2) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 37 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1|((2(-1(-3x)^2 + 5(-3x) - 1) + 2)/(2(-1(-3x)^2 + 5(-3x) - 1) - 3)) - 2| - 2 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) = 1sin(2π(-3(3|((-2x)/(2x - 1))| - 3)^2 + 1(3|((-2x)/(2x - 1))| - 3) - 5) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 172 | MATH |
[
{
"content": "How many zeros does the function f(x) = (3(-3sin(3π(2|(4x^2 + 3x - 5) + 1| - 3)) + 1) + 1)/(-2(-3sin(3π(2|(4x^2 + 3x - 5) + 1| - 3)) + 1) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 908 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3(-1((3(-3|x - 2|) - 1)/(-3(-3|x - 2|) - 3))^2 + 5((3(-3|x - 2|) - 1)/(-3(-3|x - 2|) - 3)) - 1)^2 + 2(-1((3(-3|x - 2|) - 1)/(-3(-3|x - 2|) - 3))^2 + 5((3(-3|x - 2|) - 1)/(-3(-3|x - 2|) - 3)) - 1) + 3 equals zero.\n\nPresent the answer in ... | 6 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3sin(2π(1(4(3x^2 - 5x)^2 + 3(3x^2 - 5x) - 3) - 3) - 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 966 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2(1|((3(5x^2 - 4x) + 1)/(3(5x^2 - 4x))) - 2| - 2) - 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 (-1(5(3cos(3π((2x)/(-3x + 1)) + 2) + 2) - 2))/(-3(5(3cos(3π((2x)/(-3x + 1)) + 2) + 2) - 2) + 2) = 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) = 2sin(1π(-2(2|((1x + 3)/(3x - 2)) - 2| + 1) + 1) - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 47 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (1(3cos(2π(-4(-5x^2 + 3x - 2)^2 + 2(-5x^2 + 3x - 2) - 3) + 2) + 1) + 1)/(-1(3cos(2π(-4(-5x^2 + 3x - 2)^2 + 2(-5x^2 + 3x - 2) - 3) + 2) + 1) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 563 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (1((-1(4(1cos(3πx + 2) + 1) - 2) - 1)/(2(4(1cos(3πx + 2) + 1) - 2) - 3)) + 2)/(2((-1(4(1cos(3πx + 2) + 1) - 2) - 1)/(2(4(1cos(3πx + 2) + 1) - 2) - 3)) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 60 | MATH |
[
{
"content": "How many solutions does the equation (3(1(2cos(1π(1x^2 + 4x + 4) - 3) + 2) - 3))/(-2(1(2cos(1π(1x^2 + 4x + 4) - 3) + 2) - 3) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 208 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3|(-2((-1(1x^2 - 1x - 1) - 2)/(-3(1x^2 - 1x - 1) + 2))) - 2| + 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 -1((-3(-1(-3sin(1πx - 1) - 2) - 1) + 2)/(1(-1(-3sin(1πx - 1) - 2) - 1) - 2))^2 - 5((-3(-1(-3sin(1πx - 1) - 2) - 1) + 2)/(1(-1(-3sin(1πx - 1) - 2) - 1) - 2)) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 20 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3|(-2e^(-2(2(4x^2 - 1x + 2)^2 + 2(4x^2 - 1x + 2))) - 1)| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(-4(4(-2|x + 2| + 3) - 1) - 2) - 1| + 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) = (2(-2cos(2π(4(-2|x - 3| - 1)^2 + 4(-2|x - 3| - 1) - 1) + 2) - 1))/(-1(-2cos(2π(4(-2|x - 3| - 1)^2 + 4(-2|x - 3| - 1) - 1) + 2) - 1) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1493 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3(-2sin(1π(3(4x^2 - 2x - 4)^2 - 2(4x^2 - 2x - 4) + 4) - 1) + 3) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 551 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (1(1cos(3π((-1(-1x^2 - 4x - 3) + 1)/(2(-1x^2 - 4x - 3) + 1)) - 1)) + 1)/(-1(1cos(3π((-1(-1x^2 - 4x - 3) + 1)/(2(-1x^2 - 4x - 3) + 1)) - 1))) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 48 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2|(-2|(4(-3cos(1πx + 3) - 2) + 5) + 2| + 2) + 3| - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many solutions does the equation (1(1|(-3(2|x| - 2) + 1) - 2| - 2) + 1)/(3(1|(-3(2|x| - 2) + 1) - 2| - 2) + 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) = (1(-3|(-1|(1x^2 + 5x + 5) - 1| + 2) + 1| + 1) + 3)/(-2(-3|(-1|(1x^2 + 5x + 5) - 1| + 2) + 1| + 1) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3(-2(-2sin(1π(3|x - 2|) - 3) - 1) - 3) + 4 equals zero.\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) = -2((-3(-3cos(2π((-3x - 2)/(2x - 3)) + 1) + 1) + 2)/(1(-3cos(2π((-3x - 2)/(2x - 3)) + 1) + 1) + 1))^2 - 3((-3(-3cos(2π((-3x - 2)/(2x - 3)) + 1) + 1) + 2)/(1(-3cos(2π((-3x - 2)/(2x - 3)) + 1) + 1) + 1)) - 1 equals zero.\n\nPresent the answer... | 51 | MATH |
[
{
"content": "How many zeros does the function f(x) = 4(2(-3(4x + 1)^2 + 2(4x + 1))^2 - 5(-3(4x + 1)^2 + 2(4x + 1)))^2 + 1(2(-3(4x + 1)^2 + 2(4x + 1))^2 - 5(-3(4x + 1)^2 + 2(4x + 1))) - 1 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|(4(3(4x^2 + 3x - 4)^2 + 5(4x^2 + 3x - 4) - 3) + 4) + 2| + 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 2sin(3π(2|(4(2|x + 2| + 3)^2 + 1(2|x + 2| + 3) + 4) + 3|) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1212 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-1(-2(3x + 2)^2 - 2(3x + 2) + 4)^2 - 5(-2(3x + 2)^2 - 2(3x + 2) + 4) - 1) + 4 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) = -2|(1((-3(3x - 5) - 3)/(-2(3x - 5) + 3))^2 + 3((-3(3x - 5) - 3)/(-2(3x - 5) + 3)) + 2) - 1| + 1 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) = -3e^(2(-3(4(-3x^2 + 3x + 5) + 1)^2 + 5(4(-3x^2 + 3x + 5) + 1) - 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) = -4(1cos(3π(-1|(-1x^2 - 2x + 2)| - 1) - 1) - 1)^2 + 4(1cos(3π(-1|(-1x^2 - 2x + 2)| - 1) - 1) - 1) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 606 | MATH |
[
{
"content": "How many solutions does the equation (2(2(-4(-3|x + 1| + 2))^2 + 5(-4(-3|x + 1| + 2)) - 1))/(-2(2(-4(-3|x + 1| + 2))^2 + 5(-4(-3|x + 1| + 2)) - 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) = -1e^(2(-1((3(-3x^2 - 5x + 1))/(-2(-3x^2 - 5x + 1) + 3))^2 - 5((3(-3x^2 - 5x + 1))/(-2(-3x^2 - 5x + 1) + 3)) - 5)) + 1 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) = 5((1(2sin(2π(-2|x - 1| + 3) + 3)) - 1)/(-3(2sin(2π(-2|x - 1| + 3) + 3)))) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 78 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(1π((1((1(3x^2 - 4) - 3)/(-3(3x^2 - 4) + 4)) + 1)/(-2((1(3x^2 - 4) - 3)/(-3(3x^2 - 4) + 4)) + 1)) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3sin(1π((-2((-3(-2|x + 2| + 2))/(-1(-2|x + 2| + 2) + 2)) + 3)/(3((-3(-2|x + 2| + 2))/(-1(-2|x + 2| + 2) + 2)) + 3)) + 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-1(1(-2|(-3sin(2πx - 2) + 1) - 1| + 3)^2 + 5(-2|(-3sin(2πx - 2) + 1) - 1| + 3) + 3))/(3(1(-2|(-3sin(2πx - 2) + 1) - 1| + 3)^2 + 5(-2|(-3sin(2πx - 2) + 1) - 1| + 3) + 3) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Y... | 80 | MATH |
[
{
"content": "How many solutions does the equation 1((1(3(-3sin(1πx - 3) - 1) - 4) + 1)/(3(3(-3sin(1πx - 3) - 1) - 4) - 1)) - 5 = 0 have in the range [-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) = -4(-1(3(3cos(3πx + 1) + 2) - 3) + 2)^2 - 1(-1(3(3cos(3πx + 1) + 2) - 3) + 2) + 1 have in the interval [-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) = 1(2|(-3(1x + 5) - 3) - 2|)^2 - 5(2|(-3(1x + 5) - 3) - 2|) + 4 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(4(2|(4x^2 + 4)| - 2) - 3) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1194 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-4(5(-1x^2 - 4x + 2)^2 + 5(-1x^2 - 4x + 2))^2 + 3(5(-1x^2 - 4x + 2)^2 + 5(-1x^2 - 4x + 2)) + 1))/(3(-4(5(-1x^2 - 4x + 2)^2 + 5(-1x^2 - 4x + 2))^2 + 3(5(-1x^2 - 4x + 2)^2 + 5(-1x^2 - 4x + 2)) + 1) - 2) equals zero.\n\nPresent the answer... | 8 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3sin(1π(4(5(1|x - 2| - 2)^2 - 3(1|x - 2| - 2) + 1)^2 + 5(5(1|x - 2| - 2)^2 - 3(1|x - 2| - 2) + 1) + 2) - 3) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1058 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(3π(4(3(3x^2 - 2x - 3)^2 + 1) + 5) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 480 | MATH |
[
{
"content": "How many solutions does the equation 2sin(3π(1|((-2((-2x - 3)/(1x)) - 2)/(3((-2x - 3)/(1x)) - 2)) - 3| + 2)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1e^(1(2|((1(5x^2 + 1x - 4) + 1)/(-3(5x^2 + 1x - 4))) + 2| - 2)) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation 2cos(3π(1(-3(-5x^2 - 5x - 2) - 2)^2 + 5) - 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 431 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3sin(3π((-2(-1(-3x - 4) - 5) - 2)/(1(-1(-3x - 4) - 5)))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2(-3|((-1(-1|x - 1| + 1))/(-1(-1|x - 1| + 1) - 2)) + 1| + 1)^2 - 5(-3|((-1(-1|x - 1| + 1))/(-1(-1|x - 1| + 1) - 2)) + 1| + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many solutions does the equation -2(-1(4(3sin(3πx + 2) - 1) - 5) + 4) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2cos(1π(-2|(-5(-2|x - 1| - 2) + 3) + 1| + 1) - 1) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 199 | MATH |
[
{
"content": "How many solutions does the equation 1(-4(-4(1|x - 2| - 2)^2 + 3(1|x - 2| - 2))^2 + 5)^2 + 4(-4(-4(1|x - 2| - 2)^2 + 3(1|x - 2| - 2))^2 + 5) - 4 = 0 have in the range [-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) = 1|(2|(5(1x^2 + 5x + 2)^2 - 3) - 1| + 2) - 3| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2cos(3π(-3((-1(-5x) - 3)/(-3(-5x) - 1)) + 1) - 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 47 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(2π(-2((-2(-3|x - 3|) - 2)/(-2(-3|x - 3|) + 3)) - 3) - 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 5(-2|((-2((2x)/(1x + 1)) - 2)/(-1((2x)/(1x + 1)))) - 1| + 1)^2 + 1(-2|((-2((2x)/(1x + 1)) - 2)/(-1((2x)/(1x + 1)))) - 1| + 1) - 5 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(3(1|(-3|x + 1| + 2)| - 2) + 4) - 2)/(-2(3(1|(-3|x + 1| + 2)| - 2) + 4) + 3) 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(-2cos(2πx + 1) + 1)^2 - 3(-2cos(2πx + 1) + 1) - 1) + 3)/(2(1(-2cos(2πx + 1) + 1)^2 - 3(-2cos(2πx + 1) + 1) - 1) - 3)) - 5 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) = (2(2|(4(1x^2 - 5x + 4)^2 - 2(1x^2 - 5x + 4)) - 2| - 2) + 1)/(2(2|(4(1x^2 - 5x + 4)^2 - 2(1x^2 - 5x + 4)) - 2| - 2) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many solutions does the equation 5((3(-3(-1|x + 3|)^2 - 1(-1|x + 3|) + 3) - 2)/(2(-3(-1|x + 3|)^2 - 1(-1|x + 3|) + 3) - 1))^2 - 4((3(-3(-1|x + 3|)^2 - 1(-1|x + 3|) + 3) - 2)/(2(-3(-1|x + 3|)^2 - 1(-1|x + 3|) + 3) - 1)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format:... | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(2π((3(-3((-1x - 2)/(3x + 3)) + 4) - 2)/(-2(-3((-1x - 2)/(3x + 3)) + 4) - 2)) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-1(-4(1sin(3π(-4x + 1) - 1) - 2) - 5) - 1)/(1(-4(1sin(3π(-4x + 1) - 1) - 2) - 5)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 117 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(5(2cos(1π(1|x + 1|) - 2) + 2)^2 + 5(2cos(1π(1|x + 1|) - 2) + 2) - 5) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2sin(3π(-1(-1|(3x^2 + 3x - 4) + 2| + 2) + 1) - 2) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 744 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (3(4((2(1|x - 1| - 3) - 2)/(3(1|x - 1| - 3) + 3))^2 + 5((2(1|x - 1| - 3) - 2)/(3(1|x - 1| - 3) + 3)) - 3) + 1)/(-2(4((2(1|x - 1| - 3) - 2)/(3(1|x - 1| - 3) + 3))^2 + 5((2(1|x - 1| - 3) - 2)/(3(1|x - 1| - 3) + 3)) - 3)) where -10 ≤ x ≤ 10.\n\nP... | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2π((-2(-1|(-5x - 3) + 2| + 1) + 2)/(2(-1|(-5x - 3) + 2| + 1) + 2)) - 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 64 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1e^(2(3|(3(1|x - 1| - 3) + 3) + 3| - 3)) + 1 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(3cos(2π(-3x^2 - 4x - 1) - 1) + 2) + 1) - 2)/(1(1(3cos(2π(-3x^2 - 4x - 1) - 1) + 2) + 1) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 528 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2|((-3(2(4x - 5)^2 - 4(4x - 5) - 1))/(2(2(4x - 5)^2 - 4(4x - 5) - 1) + 3)) - 2| + 2 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) = -1((-2(2cos(1π((1x - 1)/(-2x + 3))) + 2) - 2)/(2(2cos(1π((1x - 1)/(-2x + 3))) + 2) - 1)) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "How many solutions does the equation 1(4(-2(-1x^2 - 5x + 5) + 1)^2 - 4(-2(-1x^2 - 5x + 5) + 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) = -1cos(3π(1(1|(2x^2 - 3x + 5) - 1| + 2) - 1) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 541 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-2((2(-2(3|x + 3| - 2)^2 + 5(3|x + 3| - 2) - 1) + 2)/(2(-2(3|x + 3| - 2)^2 + 5(3|x + 3| - 2) - 1) - 3)) - 2)/(-2((2(-2(3|x + 3| - 2)^2 + 5(3|x + 3| - 2) - 1) + 2)/(2(-2(3|x + 3| - 2)^2 + 5(3|x + 3| - 2) - 1) - 3)) - 3) have in the interval [-10, 10]?\n\nPre... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1(-3(-1(3x^2 - 4x - 4) + 4)^2 - 4(-1(3x^2 - 4x - 4) + 4) + 5) - 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) = (1(-1|(4(-1|x - 1| + 3)^2 + 5(-1|x - 1| + 3) - 1) - 2| + 2) + 3)/(-1(-1|(4(-1|x - 1| + 3)^2 + 5(-1|x - 1| + 3) - 1) - 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) = -2|(-2|(1sin(3π(2|x| + 1) + 1)) + 1| - 3) + 3| + 1 have in the interval [-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) = (1(1|(-5(-1cos(1πx + 2) + 2) + 3) + 3| - 1) - 2)/(-1(1|(-5(-1cos(1πx + 2) + 2) + 3) + 3| - 1) - 3) where -10 ≤ x ≤ 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(-5(-3sin(2π(-3x^2 - 1x + 4) + 3) - 2) - 5) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1115 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1cos(2π(-2|(2(-2|x - 1| + 2) + 3) - 1| - 1) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 157 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3|((2(3(3|x - 1| - 1) - 5) - 3)/(3(3(3|x - 1| - 1) - 5) - 1)) + 2| + 1 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(-2((1(2cos(3πx - 2) + 1) + 2)/(1(2cos(3πx - 2) + 1) - 2))^2 - 4((1(2cos(3πx - 2) + 1) + 2)/(1(2cos(3πx - 2) + 1) - 2)) - 1))/(-1(-2((1(2cos(3πx - 2) + 1) + 2)/(1(2cos(3πx - 2) + 1) - 2))^2 - 4((1(2cos(3πx - 2) + 1) + 2)/(1(2cos(3πx - 2) + 1) - 2)) - 1) + ... | 60 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1((1((-3(-2sin(3πx + 3) - 3) + 2)/(-3(-2sin(3πx + 3) - 3) - 2)) - 2)/(3((-3(-2sin(3πx + 3) - 3) + 2)/(-3(-2sin(3πx + 3) - 3) - 2)) + 3))^2 - 5((1((-3(-2sin(3πx + 3) - 3) + 2)/(-3(-2sin(3πx + 3) - 3) - 2)) - 2)/(3((-3(-2sin(3πx + 3) - 3) + 2)/(-3(-2sin(3πx +... | 60 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3((1(3(-1|x + 2| + 2)^2 - 2(-1|x + 2| + 2) - 2) + 1)/(3(3(-1|x + 2| + 2)^2 - 2(-1|x + 2| + 2) - 2) - 1)) + 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) = 1|(-2|((-3(-2sin(2πx + 1) + 2) - 1)/(-2(-2sin(2πx + 1) + 2) - 2)) - 1|) - 2| - 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) = 3(-3|(1(-2x^2 - 3x)^2 + 5(-2x^2 - 3x) - 3) - 2|) + 5 where -10 ≤ x ≤ 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(3(-2cos(2π(5x + 4) - 3) + 1) - 4) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3|(1sin(2π((-3(-3|x + 2| + 3) + 2)/(1(-3|x + 2| + 3) + 3)) - 1) - 3) + 3| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | MATH |
[
{
"content": "How many zeros does the function f(x) = -4(3((-1(-1|x + 1| + 3) + 1)/(1(-1|x + 1| + 3) - 2))^2 - 4((-1(-1|x + 1| + 3) + 1)/(1(-1|x + 1| + 3) - 2)) + 1) 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) = -3|(4((2(3x^2 - 2x - 3) + 2)/(-3(3x^2 - 2x - 3) + 2)) + 2) - 1| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation (-1(-2|(2|(2sin(2πx + 2))| + 1) - 2| - 2) - 2)/(1(-2|(2|(2sin(2πx + 2))| + 1) - 2| - 2)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54 | MATH |
[
{
"content": "How many solutions does the equation 3|(-1cos(2π((2(-1|x + 1|) - 3)/(2(-1|x + 1|))) + 2) + 2) - 3| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61 | MATH |
[
{
"content": "How many solutions does the equation 2(4(-2|((2x - 2)/(-2x - 3)) + 3| + 2) - 2)^2 + 1(4(-2|((2x - 2)/(-2x - 3)) + 3| + 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": "Find the number of x-intercepts of the function f(x) = 2|(-2e^(-1(5(2|x + 2|) - 5)) + 2) + 2| - 3 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(-4(4x^2 - 4x - 4)^2 + 2(4x^2 - 4x - 4) + 4) + 1)/(-2(-4(4x^2 - 4x - 4)^2 + 2(4x^2 - 4x - 4) + 4) - 3))) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many solutions does the equation -5((-1(-2cos(3π(-2|x + 3| + 3) + 3)) - 2)/(2(-2cos(3π(-2|x + 3| + 3) + 3)) - 3))^2 + 5((-1(-2cos(3π(-2|x + 3| + 3) + 3)) - 2)/(2(-2cos(3π(-2|x + 3| + 3) + 3)) - 3)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 180 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-1(3cos(1π(2|((3x)/(-1x - 3))| + 2) - 2) - 1) + 1)/(-2(3cos(1π(2|((3x)/(-1x - 3))| + 2) - 2) - 1) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 65 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -5(-1((-2(2|x + 1| - 1) - 1)/(-1(2|x + 1| - 1) + 2)) - 4)^2 + 1(-1((-2(2|x + 1| - 1) - 1)/(-1(2|x + 1| - 1) + 2)) - 4) + 2 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) = -3(-1(5(3x^2 + 3x)^2 - 1(3x^2 + 3x) + 2)^2 + 4(5(3x^2 + 3x)^2 - 1(3x^2 + 3x) + 2) + 5) + 4 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) = 1|(-2|(1(3sin(2πx - 1) - 2) + 1) - 3| + 1) + 3| - 2 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) = -2|(2|(-4(-4x^2 + 4x + 1)^2 - 5(-4x^2 + 4x + 1) + 1) + 1|) - 1| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
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