messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "How many solutions does the equation 3(2cos(3π(-2|(1x + 5) + 1| - 1) - 2) + 3)^2 - 4 = 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 3sin(1π(-5((-1(4x - 4))/(-2(4x - 4) + 3))^2 - 3((-1(4x - 4))/(-2(4x - 4) + 3)) - 4) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(1π(2|((-3(1x + 3) + 3)/(2(1x + 3) - 3)) - 1| + 3) - 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "How many zeros does the function f(x) = (2(2|(2cos(1πx - 1)) - 2| - 3) + 3)/(-1(2|(2cos(1πx - 1)) - 2| - 3) + 2) 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) = -3sin(3π(3((-2(-1x^2 + 5x - 4) + 3)/(3(-1x^2 + 5x - 4) + 2)) - 5) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 130 | MATH |
[
{
"content": "How many solutions does the equation 3cos(3π(1(3((-1x + 2)/(1x + 1)) - 3)^2 - 5(3((-1x + 2)/(1x + 1)) - 3) - 3) - 3) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 371 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(2π(-4(-1|x - 3|) - 1) - 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-2(-1sin(2π(2(3|x - 3| + 2)^2 - 2(3|x - 3| + 2) + 4) - 2) - 1) - 3)/(3(-1sin(2π(2(3|x - 3| + 2)^2 - 2(3|x - 3| + 2) + 4) - 2) - 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1098 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 4(-1sin(2π((-3(1|x + 2|) - 3)/(1(1|x + 2|))) - 2) - 2)^2 + 4(-1sin(2π((-3(1|x + 2|) - 3)/(1(1|x + 2|))) - 2) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2cos(1π(-3(1|(-2x - 3) + 2| - 3)^2 - 4(1|(-2x - 3) + 2| - 3) + 1) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1302 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (2(2sin(2π(5x - 1) + 3) + 2) - 3)/(-1(2sin(2π(5x - 1) + 3) + 2) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (3(1|(1sin(1πx - 3)) + 1| - 1) + 2)/(3(1|(1sin(1πx - 3)) + 1| - 1) - 1) 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) = (-2(-2cos(3π(4x - 4) - 3) + 1) + 1)/(1(-2cos(3π(4x - 4) - 3) + 1) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(-3sin(2π((1x - 1)/(3x - 1)) + 1)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(-3sin(3π((2x - 3)/(-1x - 2)) - 2))^2 + 1(-3sin(3π((2x - 3)/(-1x - 2)) - 2)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 228 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1|(-1(-1(-2cos(1πx - 1)) - 3)^2 + 5(-1(-2cos(1πx - 1)) - 3) + 5) + 1| + 1 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) = 1(1sin(2π(2|((2x + 1)/(-1x + 2)) - 2|) - 2) - 2)^2 + 2(1sin(2π(2|((2x + 1)/(-1x + 2)) - 2|) - 2) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 154 | MATH |
[
{
"content": "How many solutions does the equation -5(-1((-2(-2cos(2πx) - 2) - 3)/(-1(-2cos(2πx) - 2) - 3))^2 - 1((-2(-2cos(2πx) - 2) - 3)/(-1(-2cos(2πx) - 2) - 3)) + 1) - 1 = 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) = -3|(-4(-3sin(1πx + 2))^2 + 3(-3sin(1πx + 2))) + 3| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many zeros does the function f(x) = (3(-4(-1sin(3π(-5x^2 + 4x + 3) + 1)) + 4) - 1)/(1(-4(-1sin(3π(-5x^2 + 4x + 3) + 1)) + 4) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 824 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2π(4(-3|(4x - 3) - 3| + 1)^2 - 1(-3|(4x - 3) - 3| + 1) - 4) + 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1110 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(2cos(3π((-1x + 3)/(3x - 1)) + 1) - 1)^2 + 5(2cos(3π((-1x + 3)/(3x - 1)) + 1) - 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | MATH |
[
{
"content": "How many solutions does the equation 1sin(2π(1(5((-3x)/(3x - 2)) + 2)^2 - 2(5((-3x)/(3x - 2)) + 2) + 4) - 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 143 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1|(-2(3cos(2πx - 1) - 3) + 1) - 1| where -10 ≤ x ≤ 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) = (1(1(3sin(2πx + 3) + 1)^2 - 5) - 1)/(1(1(3sin(2πx + 3) + 1)^2 - 5) + 2) 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|(5(-2sin(2πx + 3) - 1)^2 - 1(-2sin(2πx + 3) - 1) - 4) - 1| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "How many solutions does the equation 2(1sin(2π(2x - 2) - 3))^2 - 2(1sin(2π(2x - 2) - 3)) - 1 = 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) = (3(-2sin(3π(-5(2|x - 1| + 2)^2 - 2(2|x - 1| + 2) - 4) + 3) - 2))/(-1(-2sin(3π(-5(2|x - 1| + 2)^2 - 2(2|x - 1| + 2) - 4) + 3) - 2) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1645 | MATH |
[
{
"content": "How many zeros does the function f(x) = 5(-3cos(3π(1x - 5)))^2 + 3(-3cos(3π(1x - 5))) - 5 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) = 1cos(1π(2(-3|((2x)/(-1x - 2)) + 3| - 3)^2 + 3(-3|((2x)/(-1x - 2)) + 3| - 3) - 1) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 564 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3cos(1π((3(1x - 3) + 3)/(3(1x - 3) - 2)) - 2) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1|(-2cos(3π((3x - 1)/(3x + 3)) - 1) + 2) - 3| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 91 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1cos(1π((1(3x - 1) - 3)/(3(3x - 1) - 1)) - 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1|(-4(3cos(3π(4x - 3)) + 2)^2 - 3(3cos(3π(4x - 3)) + 2) + 4) + 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 132 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1(3cos(3π(-2|x - 3| + 3) + 1) - 2) - 1)/(3(3cos(3π(-2|x - 3| + 3) + 1) - 2) - 2) 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 1sin(2π(1((-2x)/(2x - 1)) + 5) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (2(2sin(2π(-1x + 1)) - 1) - 1)/(1(2sin(2π(-1x + 1)) - 1) + 2) 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|(-2e^(2(2x + 4)) + 1) - 3| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "How many solutions does the equation 2sin(2π((2(1(-1|x - 3| - 2)^2 + 1(-1|x - 3| - 2) - 2) + 3)/(1(1(-1|x - 3| - 2)^2 + 1(-1|x - 3| - 2) - 2))) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 5(-2sin(1π(2x - 5) + 3) - 2)^2 + 5(-2sin(1π(2x - 5) + 3) - 2) + 1 where -10 ≤ x ≤ 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|((-2(2sin(1π(1x^2 + 2x + 2) + 1)) + 2)/(3(2sin(1π(1x^2 + 2x + 2) + 1)) + 3)) - 3| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 279 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2π((-2(-4x - 5))/(2(-4x - 5) - 3)) + 1) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "How many zeros does the function f(x) = (1(1sin(2π(-3x^2 - 3x - 2) + 1) - 2) + 1)/(-3(1sin(2π(-3x^2 - 3x - 2) + 1) - 2) + 4) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 561 | MATH |
[
{
"content": "How many solutions does the equation -5(-1cos(2π(-2|x| - 2)))^2 + 3(-1cos(2π(-2|x| - 2))) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "How many solutions does the equation (1(-5(2sin(2πx - 1)) + 5))/(-1(-5(2sin(2πx - 1)) + 5) - 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 4(1cos(1π(-1|(-4x - 2) - 2| + 2) - 1))^2 - 2(1cos(1π(-1|(-4x - 2) - 2| + 2) - 1)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 159 | MATH |
[
{
"content": "How many solutions does the equation 3sin(3π((-3(-2x^2 + 1x - 5) - 1)/(1(-2x^2 + 1x - 5) + 2)) - 3) + 3 = 0 have in the range [-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) = 2cos(3π(1(-1x^2 - 5) + 2) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 600 | MATH |
[
{
"content": "How many solutions does the equation 3cos(3π(5(-1|((-1x + 3)/(2x)) + 1| + 3)^2 + 1(-1|((-1x + 3)/(2x)) + 1| + 3) - 4) + 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 169 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2(-3|(-2cos(3π(-3x - 2) - 3) - 2)| + 1)^2 + 5(-3|(-2cos(3π(-3x - 2) - 3) - 2)| + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 360 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2cos(2π(2(-3|((-3x + 3)/(3x + 1)) + 2| + 3) - 4) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 140 | MATH |
[
{
"content": "How many solutions does the equation 3(-2cos(1π(4((1x - 1)/(-1x - 3))^2 - 2((1x - 1)/(-1x - 3)) + 3)) + 1) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 276 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2|((-3(-3cos(3πx - 2) - 3) + 1)/(1(-3cos(3πx - 2) - 3))) + 2| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3|(1cos(1π((-3(-5x^2 - 1x + 1) + 2)/(3(-5x^2 - 1x + 1) + 1)) + 1) - 2)| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(2cos(3π(-5((2x)/(2x + 3))^2 + 2((2x)/(2x + 3)) + 3) + 2))| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43 | MATH |
[
{
"content": "How many solutions does the equation 3sin(3π(-1|((2x - 1)/(1x + 1)) - 2| - 3) - 1) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1|(1sin(3π((1x + 2)/(-2x - 3))) + 2) - 1| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(1sin(2π(-4x^2 + 5x - 5) - 1)) - 3)/(-1(1sin(2π(-4x^2 + 5x - 5) - 1))) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 778 | MATH |
[
{
"content": "How many zeros does the function f(x) = -4(1cos(3π(1((2x + 3)/(3x + 2))^2) - 2) - 2) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2(-1cos(3π((-2x + 2)/(2x - 1))) + 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 47 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3cos(1π(-5(2((1x + 3)/(-2x - 3))^2 - 2((1x + 3)/(-2x - 3)) - 4) - 1) - 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 86 | MATH |
[
{
"content": "How many solutions does the equation -3((-3(2|(-2cos(2πx - 3) - 3) + 1| - 2))/(-2(2|(-2cos(2πx - 3) - 3) + 1| - 2) + 3))^2 - 3((-3(2|(-2cos(2πx - 3) - 3) + 1| - 2))/(-2(2|(-2cos(2πx - 3) - 3) + 1| - 2) + 3)) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your a... | 40 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2π(2|(-5x - 5) + 3|) - 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "How many solutions does the equation 2sin(3π(3|((-2x)/(-3x + 2)) - 1| + 1)) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (3(1(-3sin(2π(-2|x + 3| - 1) + 1) + 3)^2 - 2(-3sin(2π(-2|x + 3| - 1) + 1) + 3) - 3) - 3)/(1(1(-3sin(2π(-2|x + 3| - 1) + 1) + 3)^2 - 2(-3sin(2π(-2|x + 3| - 1) + 1) + 3) - 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 80 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (2(3sin(1π(2x + 3) - 3) + 1) + 1)/(-1(3sin(1π(2x + 3) - 3) + 1) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many solutions does the equation -5(-3sin(2π(-3|x + 2| - 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": "How many zeros does the function f(x) = 2(1cos(3π(-3|((1x + 2)/(-1x)) - 1|) - 2) - 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 155 | MATH |
[
{
"content": "How many solutions does the equation 3sin(1π((2(4x^2 - 5x - 3) + 1)/(1(4x^2 - 5x - 3))) + 1) + 3 = 0 have in the range [-10, 10]?\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) = (-2(5(-3sin(3πx - 3) + 3)^2 - 5(-3sin(3πx - 3) + 3) - 4) - 1)/(-2(5(-3sin(3πx - 3) + 3)^2 - 5(-3sin(3πx - 3) + 3) - 4)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3(2|(3cos(1πx + 3) + 3) + 1| - 1)^2 - 1(2|(3cos(1πx + 3) + 3) + 1| - 1) - 4 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) = -3|(2((-1(1cos(2πx + 3)) + 3)/(-3(1cos(2πx + 3)) - 2))^2 - 2) - 2| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3(-3(3cos(1πx + 2) - 3) - 5)^2 - 5(-3(3cos(1πx + 2) - 3) - 5) + 2 have in the interval [-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) = -2sin(2π((2(1(1|x - 3| + 2)^2 - 1(1|x - 3| + 2) - 4) + 1)/(-1(1(1|x - 3| + 2)^2 - 1(1|x - 3| + 2) - 4))) + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2|(-1cos(1π((2x - 1)/(-3x + 1)) + 1)) + 2| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-2(1(-3sin(3πx - 2) + 1)) - 2)/(-3(1(-3sin(3πx - 2) + 1)) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2sin(2π(2(1|(4x^2 + 5x - 3) - 1| + 2) - 2) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1473 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -4(-3sin(1π(1(-1|x - 2| - 2)^2 + 5(-1|x - 2| - 2) - 1) + 1) - 2) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 192 | MATH |
[
{
"content": "How many solutions does the equation 1|(-1cos(3π(-4(3x^2 + 1x - 3) + 1) - 2) + 1) - 1| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1232 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2sin(3π((-1(4(-1x^2 + 5x + 3) + 5) + 3)/(3(4(-1x^2 + 5x + 3) + 5) + 3))) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(3π((2(-2|x - 2|) + 1)/(-2(-2|x - 2|) + 3)) - 2) - 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) = 3sin(2π(-1|(2x^2 - 4x - 3) + 1| - 3) + 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 766 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3π(1((-1(3|x - 1| - 3) - 2)/(1(3|x - 1| - 3) - 2))^2 - 3((-1(3|x - 1| - 3) - 2)/(1(3|x - 1| - 3) - 2)) - 2) - 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 165 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3sin(3π(-2|(-3(-2x^2 + 4x + 2) + 2) - 1| + 3) + 3) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1043 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(1π(-4((3(4x^2 + 5x - 1) + 1)/(1(4x^2 + 5x - 1) - 3))) + 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 83 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1sin(2π(3(-1|(-3x - 4) - 3| + 2)^2 + 5(-1|(-3x - 4) - 3| + 2) + 3) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1058 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1cos(1π(-2(-1x^2 + 3x - 3) - 4) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 199 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1sin(1π(3((1x - 3)/(-2x - 2)) + 1) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(-3cos(2π(1|x - 3| - 3) + 1) - 1))/(-3(-3cos(2π(1|x - 3| - 3) + 1) - 1) - 2) 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) = -4(-2sin(3π(-1|x - 1| - 3) - 3) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 58 | MATH |
[
{
"content": "How many solutions does the equation -2cos(3π(-3|(-3((2x - 3)/(-1x + 3)) + 5) - 3| - 3) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 322 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1cos(2π(2|(4(-5x^2) - 3) - 1| + 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1536 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1((-3(-3|(-5x^2 - 3x - 1) - 1| + 1) - 3)/(1(-3|(-5x^2 - 3x - 1) - 1| + 1) + 1)) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 826 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3cos(1π((2(-5x^2 + 5x - 2) - 3)/(-3(-5x^2 + 5x - 2) - 1)) + 1) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many solutions does the equation 5(3sin(2π(-4((2x + 2)/(-3x + 2)) - 2) + 1) - 3)^2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 74 | MATH |
[
{
"content": "How many zeros does the function f(x) = -5(2cos(1π(-4(2|x + 1| + 1)^2 + 1(2|x + 1| + 1) + 5) + 2) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1425 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(-4(1cos(2πx - 2) - 1)^2 - 3(1cos(2πx - 2) - 1) + 3) + 3| - 2 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) = 2sin(2π(-1(-3|x| - 2)^2 - 5(-3|x| - 2) - 2) - 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1440 | MATH |
[
{
"content": "How many zeros does the function f(x) = (3(2(3cos(2π(-3|x + 3| - 1) + 1) + 3)^2 - 3(3cos(2π(-3|x + 3| - 1) + 1) + 3) - 4) - 2)/(3(2(3cos(2π(-3|x + 3| - 1) + 1) + 3)^2 - 3(3cos(2π(-3|x + 3| - 1) + 1) + 3) - 4)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 53 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -5((2(-3cos(3πx - 2) - 2) + 2)/(1(-3cos(3πx - 2) - 2) + 3)) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
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