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) = -4(-4(-2sin(1πx - 2) + 2)^2 + 5(-2sin(1πx - 2) + 2) + 3) + 4 equals zero.\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) = -2sin(3π(4(-2x + 3)^2 - 5(-2x + 3) + 3) + 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1114 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-2((-2(3cos(1πx + 3) + 3) + 2)/(1(3cos(1πx + 3) + 3))) - 2)/(3((-2(3cos(1πx + 3) + 3) + 2)/(1(3cos(1πx + 3) + 3))) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many solutions does the equation -3cos(2π(-5((3x - 1)/(1x))^2 + 2((3x - 1)/(1x)) + 3) - 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 233 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(2π(4(1|x + 3| - 2)^2 - 2)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 525 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(2π(-1|(2|x - 1| + 1) - 2| + 1) - 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many solutions does the equation 2sin(3π(1(5x^2 - 3x + 5)^2 + 4(5x^2 - 3x + 5) - 4)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 803 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -5(-2(2|x + 3| - 2)^2 - 4(2|x + 3| - 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 2cos(3π(-4((1x + 1)/(-3x + 1)) + 1) + 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 77 | MATH |
[
{
"content": "How many solutions does the equation 2sin(3π((-3(1|x + 1| + 3) + 3)/(-1(1|x + 1| + 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) = 1(-3sin(3π(1|x + 1| - 3)) - 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
[
{
"content": "How many solutions does the equation (1(2cos(1π((2x - 1)/(1x)) + 2) - 1) - 1)/(2(2cos(1π((2x - 1)/(1x)) + 2) - 1)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "How many solutions does the equation 2|(1(3x^2 - 3x - 2)^2 + 5(3x^2 - 3x - 2) + 1) - 2| - 2 = 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) = 2sin(2π((-2(-5x - 2))/(-1(-5x - 2) + 2))) where -10 ≤ x ≤ 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) = 2|(-1((3x - 2)/(3x + 2))^2 + 3((3x - 2)/(3x + 2)) + 2) + 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) = 2cos(2π(1(1x^2 + 2x - 5)^2 + 5) + 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 966 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3cos(1π((3(-1x^2 + 5x - 4) + 2)/(-3(-1x^2 + 5x - 4) + 4)) - 2) + 3 have in the interval [-10, 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) = 2sin(2π(4(5x - 4)^2 - 2(5x - 4) + 2) + 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1450 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2|(1sin(3π(1|x + 3| - 1))) + 2| - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 62 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2(-1|(2x^2 - 4x + 1) - 2| + 3)^2 - 3(-1|(2x^2 - 4x + 1) - 2| + 3) + 1 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 1cos(3π(1|((2x - 2)/(-1x + 2)) + 1|) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "How many solutions does the equation 3sin(1π((1((-1x + 2)/(1x + 3)) + 1)/(-1((-1x + 2)/(1x + 3)) - 3)) - 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45 | MATH |
[
{
"content": "How many solutions does the equation 4(-4(4x^2 - 1x - 5)^2 - 2(4x^2 - 1x - 5) + 5)^2 + 4(-4(4x^2 - 1x - 5)^2 - 2(4x^2 - 1x - 5) + 5) - 5 = 0 have in the range [-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|(4(-4x^2 - 5x + 5) - 2) + 2| - 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) = (1(-2(1x^2 + 1x - 3)^2 + 3(1x^2 + 1x - 3) + 1) + 2)/(3(-2(1x^2 + 1x - 3)^2 + 3(1x^2 + 1x - 3) + 1) - 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) = -2|(-2|(2cos(2πx + 3) - 3) + 2| + 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) = -3cos(3π(3(-1x^2 - 3x - 3)^2 - 1(-1x^2 - 3x - 3) - 3) + 3) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1173 | MATH |
[
{
"content": "How many solutions does the equation -3cos(2π((-2((-3x - 2)/(-1x - 3)) + 2)/(-2((-3x - 2)/(-1x - 3)) + 3))) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "How many solutions does the equation (-2(-3(-3cos(1πx - 1) + 1) - 4) - 1)/(1(-3(-3cos(1πx - 1) + 1) - 4) + 2) = 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) = -1(-3cos(1π(4x^2 + 5x - 1) - 1) + 2)^2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 677 | MATH |
[
{
"content": "How many solutions does the equation 1|(-3(-5x^2 + 2x + 1)^2 - 3(-5x^2 + 2x + 1) + 1) - 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) = 2(-2|(1x^2 - 5x) - 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 solutions does the equation -3cos(2π(-1(2x^2 + 5x - 1) + 4) + 1) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 354 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2(-5(3x^2 + 5x - 3)^2 - 2(3x^2 + 5x - 3) + 2) + 3 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) = 3cos(1π(5((-1x - 1)/(2x + 3)) + 4) - 1) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "How many solutions does the equation 3sin(3π(-4(-3|x + 1| + 3)^2 + 3(-3|x + 1| + 3) + 3) + 1) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1131 | MATH |
[
{
"content": "How many solutions does the equation (-2(1|(-3sin(2πx - 3)) + 1| - 2) - 1)/(-2(1|(-3sin(2πx - 3)) + 1| - 2) - 3) = 0 have in the range [-10, 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|((2(3|x + 2| - 3) + 3)/(-2(3|x + 2| - 3) - 1)) + 3| + 3 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|(-1|(-4x^2 + 3x + 3) + 1| + 3) - 2| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "How many solutions does the equation -1cos(1π(3(-1x)^2 - 1(-1x) - 4) + 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 286 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 4((3(3sin(3πx) - 2) - 2)/(3(3sin(3πx) - 2) - 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 -2(1(1cos(2πx - 3) - 3)^2 + 3(1cos(2πx - 3) - 3) + 2)^2 - 2(1(1cos(2πx - 3) - 3)^2 + 3(1cos(2πx - 3) - 3) + 2) + 4 = 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) = 1(-2(1cos(2πx + 3) - 2)^2 + 4(1cos(2πx + 3) - 2) + 3)^2 + 3(-2(1cos(2πx + 3) - 2)^2 + 4(1cos(2πx + 3) - 2) + 3) - 5 have in the interval [-10, 10]?\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) = (-2(-2|(3sin(2πx + 1)) - 1| + 1) - 1)/(1(-2|(3sin(2πx + 1)) - 1| + 1)) 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 -2cos(1π(5((2x - 3)/(-1x))^2 - 1((2x - 3)/(-1x)) + 2) + 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 257 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 5(-4(3sin(2πx + 1) - 1) + 1)^2 - 4(-4(3sin(2πx + 1) - 1) + 1) - 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(3sin(1π((2x - 2)/(1x - 2)) - 2) + 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-2cos(2π((3x + 1)/(-1x + 3)) + 3) + 2) + 3)/(-2(-2cos(2π((3x + 1)/(-1x + 3)) + 3) + 2) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 117 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3cos(2π(2|((-1x - 3)/(-2x - 2)) + 3| + 2) - 2) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 65 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(2(-1x^2 + 2x + 5)^2 + 2(-1x^2 + 2x + 5) - 3) - 3 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) = 2|(-4(-1|x - 3| + 2) + 3) + 1| - 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(-3sin(1π((-1x + 2)/(1x)) - 3) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 49 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2sin(1π(3(1x^2 + 2x + 3) + 3) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 604 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 4(5(-1|x + 2| + 2) + 2)^2 + 4(5(-1|x + 2| + 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|(2cos(3π((1x - 2)/(1x)) + 2)) - 3| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 85 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (2(2cos(3π(-4x - 2) - 1) - 2) + 1)/(-3(2cos(3π(-4x - 2) - 1) - 2) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "How many solutions does the equation (1(-2cos(1π((2x - 3)/(-3x - 2)) + 1) - 2) + 2)/(-2(-2cos(1π((2x - 3)/(-3x - 2)) + 1) - 2) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2(2(3|x - 3| - 2)^2 + 1(3|x - 3| - 2) - 4) + 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) = -4(2cos(1π(2|x + 1| + 1) + 3)) - 5 have in the interval [-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) = 2cos(3π(1|(-3|x - 3|) + 1| + 2) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-3(2cos(3π(-1x + 5) + 2) - 2) - 3)/(2(2cos(3π(-1x + 5) + 2) - 2) - 1) have in the interval [-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) = 1cos(2π(-1(3|x + 1| + 3)^2 - 4) - 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1275 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -5(2sin(3π(-2|x - 1| - 1) - 3) - 1) + 5 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) = -3sin(1π(-1|(-1x^2 + 4x + 4) - 3| - 3) - 2) + 2 equals zero.\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) = (-2(-1(-2cos(2πx - 2) - 2)^2 - 1(-2cos(2πx - 2) - 2) + 2) - 3)/(1(-1(-2cos(2πx - 2) - 2)^2 - 1(-2cos(2πx - 2) - 2) + 2) + 1) 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 2cos(1π(1(2|x + 3| - 2) - 3) + 3) + 2 = 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) = -2cos(2π((-1(-1x^2 - 5x) - 3)/(-3(-1x^2 - 5x) - 1)) - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2(3sin(3π(1x^2 - 4x - 1) + 2) + 1)^2 - 2(3sin(3π(1x^2 - 4x - 1) + 2) + 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1096 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2|(-1(-3sin(2πx + 3) - 3) + 1) - 2| - 1 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) = -3|(4(-3x^2 - 3x + 4)^2 + 4(-3x^2 - 3x + 4) - 4) - 1| + 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) = 1(2|(-2sin(3πx + 1) + 2)| - 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) = -2sin(1π(-1|((2x)/(3x + 3)) + 1| + 2)) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(1π(2(-5x^2 - 2x - 5)^2 - 5(-5x^2 - 2x - 5)) - 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 849 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2|(-1((-1x + 2)/(-1x + 3))^2 - 1((-1x + 2)/(-1x + 3)) + 5) - 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 -2|(-1|(2cos(3πx + 1) + 1)| + 2) + 1| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "How many solutions does the equation (1(-2sin(1π(-2|x + 2| + 2) + 2) - 3) + 1)/(-2(-2sin(1π(-2|x + 2| + 2) + 2) - 3) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many solutions does the equation -2cos(2π(-2(2x^2 - 2x + 4)^2 - 1(2x^2 - 2x + 4) + 3) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1494 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(-2|(-2sin(3πx) - 1) + 3| - 3) + 3| - 3 equals zero.\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) = (-1(2sin(1π(-4x - 1)) - 1))/(-3(2sin(1π(-4x - 1)) - 1) - 3) 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) = -5(-3cos(2π(1x^2 + 2x - 5) + 2) - 1)^2 + 5(-3cos(2π(1x^2 + 2x - 5) + 2) - 1) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 751 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1|(3sin(3π(-5x^2) + 3) - 1) - 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1643 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2(-2sin(2π((3x + 2)/(2x + 2)) + 1) - 2)^2 - 4(-2sin(2π((3x + 2)/(2x + 2)) + 1) - 2) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 35 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1((2(-3cos(2πx - 2) - 2) - 1)/(-1(-3cos(2πx - 2) - 2) - 1))^2 - 2((2(-3cos(2πx - 2) - 2) - 1)/(-1(-3cos(2πx - 2) - 2) - 1)) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many solutions does the equation 1((-2(-1sin(3πx + 1) + 1) - 3)/(2(-1sin(3πx + 1) + 1) - 1))^2 - 4((-2(-1sin(3πx + 1) + 1) - 3)/(2(-1sin(3πx + 1) + 1) - 1)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many solutions does the equation 2|(-1sin(2π(4x - 2)))| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 109 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2|(2cos(3π(3x^2 - 5x + 5) - 3) + 3) - 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1434 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(4(-1x^2 + 5x - 1) - 4)^2 + 2(4(-1x^2 + 5x - 1) - 4) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation -2|(3(-2e^(1x) + 2)^2 - 3(-2e^(1x) + 2) - 3) + 2| + 1 = 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) = -1sin(3π(5((3x + 3)/(1x))^2 + 3((3x + 3)/(1x)) - 4) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 294 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(3π((-1(5x + 1) + 3)/(-1(5x + 1) - 2)) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 63 | MATH |
[
{
"content": "How many solutions does the equation 3(5(2e^(-2x) - 3)^2 - 4)^2 + 5(5(2e^(-2x) - 3)^2 - 4) - 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) = 3sin(2π(-2(4x^2 - 4x + 5) + 1) + 2) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1091 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1sin(1π(5(1|x - 3| + 1)^2 + 1(1|x - 3| + 1) - 3) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1226 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3(3sin(3π(4x^2 + 3x - 5) + 2))^2 + 1(3sin(3π(4x^2 + 3x - 5) + 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 201 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-2(1cos(3π(3|x + 3| - 1)) - 1) - 3)/(2(1cos(3π(3|x + 3| - 1)) - 1) + 2) have in the interval [-10, 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) = 3e^(1(-3(-1x^2 + 5x - 5)^2 - 4(-1x^2 + 5x - 5) - 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|(3cos(2π(2|x - 2| - 2)) - 1) - 1| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many solutions does the equation 1cos(2π(-4((2x + 2)/(3x - 1))^2 + 3((2x + 2)/(3x - 1)) - 3) - 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 79 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2(5(-2sin(1πx - 3) - 3) + 5) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many solutions does the equation -3|(3|(5x^2 + 3x + 2) - 2|)| + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
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