messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-3(-1sin(2π((1x - 3)/(-1x + 2)) - 1))) + 3)/(-1(-3(-1sin(2π((1x - 3)/(-1x + 2)) - 1)))) equals zero.\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) = 3cos(3π(5((3(-2x - 4) - 2)/(-2(-2x - 4) + 3)) - 5)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 109 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3(2|(-1|(5x - 5) + 2| + 2) + 2| - 1) + 5 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((-2(1(-3cos(2πx - 2) + 2)) - 2)/(3(1(-3cos(2πx - 2) + 2)) - 2))^2 + 5((-2(1(-3cos(2πx - 2) + 2)) - 2)/(3(1(-3cos(2πx - 2) + 2)) - 2)) - 1 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) = -1(-1|(-2(3cos(3πx + 2) - 3) - 5) - 1| + 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many solutions does the equation -2sin(3π(-2|(2|(-1|x - 2| + 1) + 1| - 3)| - 3) + 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1cos(3π((2(-1((-1x - 1)/(2x + 3))^2 - 3((-1x - 1)/(2x + 3)) + 5))/(1(-1((-1x - 1)/(2x + 3))^2 - 3((-1x - 1)/(2x + 3)) + 5) + 1)) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3|(-3|((-1((2x + 2)/(1x)) + 3)/(-3((2x + 2)/(1x)) + 2)) + 3| + 2) + 3| - 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) = 4(1(-3|(1x^2 - 3x) + 1|)^2 - 4(-3|(1x^2 - 3x) + 1|) - 1) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation (-2(1((-3(2|x - 1| - 3) + 2)/(-1(2|x - 1| - 3) + 2))^2 - 3((-3(2|x - 1| - 3) + 2)/(-1(2|x - 1| - 3) + 2)) - 1) + 2)/(-2(1((-3(2|x - 1| - 3) + 2)/(-1(2|x - 1| - 3) + 2))^2 - 3((-3(2|x - 1| - 3) + 2)/(-1(2|x - 1| - 3) + 2)) - 1)) = 0 have in the range [-10, 10]?\... | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = -5((2(2cos(1π(-1x - 5) + 2) + 2) - 2)/(3(2cos(1π(-1x - 5) + 2) + 2) + 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 solutions does the equation -2|(-2sin(1π(-2((2x + 1)/(2x + 3)) - 5) - 1) + 3)| + 3 = 0 have in the range [-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) = -4(-3|(-2|(2cos(3πx)) + 1| + 2)| + 1)^2 - 5(-3|(-2|(2cos(3πx)) + 1| + 2)| + 1) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 340 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1|((-2(-2e^(1(4x^2 + 1x)) + 2) + 3)/(3(-2e^(1(4x^2 + 1x)) + 2) + 1)) - 1| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = 4(5(2(2|x - 1| - 2)^2 - 5(2|x - 1| - 2) - 5) - 3)^2 - 2(5(2(2|x - 1| - 2)^2 - 5(2|x - 1| - 2) - 5) - 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(3(-3sin(1π((1x)/(-3x - 2))) + 3)^2 + 3(-3sin(1π((1x)/(-3x - 2))) + 3) - 1) + 1| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "How many solutions does the equation 1(-1|(5(-2x^2 + 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) = (-2(4(2(-2cos(1πx - 2) - 1)^2 + 2(-2cos(1πx - 2) - 1) - 1)^2 + 1(2(-2cos(1πx - 2) - 1)^2 + 2(-2cos(1πx - 2) - 1) - 1) - 2))/(1(4(2(-2cos(1πx - 2) - 1)^2 + 2(-2cos(1πx - 2) - 1) - 1)^2 + 1(2(-2cos(1πx - 2) - 1)^2 + 2(-2cos(1πx - 2) - 1) - 1) - ... | 80 | MATH |
[
{
"content": "How many solutions does the equation 5(-2|(1((1x)/(2x - 1))^2 + 1((1x)/(2x - 1))) - 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 solutions does the equation 3(-4(2(2|x - 3| - 1)^2 - 4(2|x - 3| - 1) - 2)^2 + 5(2(2|x - 3| - 1)^2 - 4(2|x - 3| - 1) - 2) + 4) - 1 = 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(5(-5((2x + 1)/(1x))^2 - 5((2x + 1)/(1x)) + 5)^2 - 1(-5((2x + 1)/(1x))^2 - 5((2x + 1)/(1x)) + 5) - 1) + 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) = -1sin(1π(2(2(1|x + 2| + 1)^2 - 5(1|x + 2| + 1) - 3) + 3)) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 363 | MATH |
[
{
"content": "How many solutions does the equation 4((3(-3cos(2π(-2x + 2) - 2) - 3))/(2(-3cos(2π(-2x + 2) - 2) - 3) - 1)) - 5 = 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) = 1(3((-2(2sin(3πx - 2) + 3))/(-1(2sin(3πx - 2) + 3) - 2))^2 + 1((-2(2sin(3πx - 2) + 3))/(-1(2sin(3πx - 2) + 3) - 2)) + 1)^2 - 5(3((-2(2sin(3πx - 2) + 3))/(-1(2sin(3πx - 2) + 3) - 2))^2 + 1((-2(2sin(3πx - 2) + 3))/(-1(2sin(3πx - 2) + 3) - 2)... | 60 | MATH |
[
{
"content": "How many zeros does the function f(x) = -4(2sin(2π(-5((3x - 1)/(-3x - 1)) + 2) + 1) - 2)^2 + 1(2sin(2π(-5((3x - 1)/(-3x - 1)) + 2) + 1) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 72 | MATH |
[
{
"content": "How many solutions does the equation 2cos(2π(2|(1((2x - 1)/(2x))^2 - 4((2x - 1)/(2x)) - 2) + 1| - 3)) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2sin(2π(-3(2|(3x^2 - 1x - 5) - 1| + 1)^2 - 3(2|(3x^2 - 1x - 5) - 1| + 1) + 5) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 622 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -5(-4(-3cos(3π((3x - 1)/(-3x - 1)) + 1)) + 2) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(-1|((-1(3x - 4) - 3)/(-3(3x - 4))) + 1| - 1) + 2| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1(-2|(-1(-3|x - 3| - 1)^2 - 4(-3|x - 3| - 1))| - 1)^2 + 5 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|((3((-3(-1x^2 + 5x + 5) - 1)/(1(-1x^2 + 5x + 5) + 3)) - 1)/(-3((-3(-1x^2 + 5x + 5) - 1)/(1(-1x^2 + 5x + 5) + 3)) + 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 solutions does the equation (-2(1(-3cos(3π(1x^2 + 1) - 2) - 2)^2 - 3(-3cos(3π(1x^2 + 1) - 2) - 2) - 4) + 1)/(-1(1(-3cos(3π(1x^2 + 1) - 2) - 2)^2 - 3(-3cos(3π(1x^2 + 1) - 2) - 2) - 4) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 392 | MATH |
[
{
"content": "How many solutions does the equation -2(4(-1(4x - 1) + 4)^2 - 2(-1(4x - 1) + 4) - 4)^2 + 1(4(-1(4x - 1) + 4)^2 - 2(-1(4x - 1) + 4) - 4) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(1π(3(-4(-3|x| - 2) - 5) - 1) - 1) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 339 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2((-1(-1(2cos(1πx - 1) + 3)^2 + 3(2cos(1πx - 1) + 3) + 2) - 3)/(-3(-1(2cos(1πx - 1) + 3)^2 + 3(2cos(1πx - 1) + 3) + 2) + 4))^2 + 2((-1(-1(2cos(1πx - 1) + 3)^2 + 3(2cos(1πx - 1) + 3) + 2) - 3)/(-3(-1(2cos(1πx - 1) + 3)^2 + 3(2cos(1πx - 1) + 3) + 2) + 4)) - 5 ... | 40 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-1(1sin(3π((3(5x - 4) - 2)/(3(5x - 4) - 1)) + 1) - 3) - 2)/(-2(1sin(3π((3(5x - 4) - 2)/(3(5x - 4) - 1)) + 1) - 3) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1(1(1((2x - 1)/(-2x + 3)) - 2)^2 - 4(1((2x - 1)/(-2x + 3)) - 2) + 2)^2 - 2(1(1((2x - 1)/(-2x + 3)) - 2)^2 - 4(1((2x - 1)/(-2x + 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) = 2((-2(2cos(3π((3x - 3)/(2x + 1)) - 3)) - 3)/(-2(2cos(3π((3x - 3)/(2x + 1)) - 3)) - 1)) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1|(2(2e^(-1(-2|x + 1| + 2)) - 3) - 1) + 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) = (3(-2|(-2|(2x - 2) + 1| + 2) + 1| + 2) + 2)/(3(-2|(-2|(2x - 2) + 1| + 2) + 1| + 2) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation -4(-2cos(2π(3(5x + 1)) + 3) - 2)^2 + 5(-2cos(2π(3(5x + 1)) + 3) - 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 600 | MATH |
[
{
"content": "How many solutions does the equation 2cos(1π((-1(-4(-2|x + 3| + 2) + 3) + 1)/(2(-4(-2|x + 3| + 2) + 3) - 1)) + 2) + 1 = 0 have in the range [-10, 10]?\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) = (-2(5(3cos(1π(2x - 5)) + 1) + 5) - 3)/(-2(5(3cos(1π(2x - 5)) + 1) + 5) + 3) 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 -2|(-1(3sin(1π(-3|x| - 2)) - 2)^2 + 2(3sin(1π(-3|x| - 2)) - 2) - 1) + 1| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "How many solutions does the equation 5(-3(3|(3|x + 1| - 3)| - 1) + 4)^2 + 4(-3(3|(3|x + 1| - 3)| - 1) + 4) - 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) = -1|(-5(3cos(2π(-3x - 5) - 2) + 2) + 4)| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 221 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2(1(2sin(3π((-1x + 3)/(-3x - 1)) + 1) - 3) + 5) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2π(5(-3|(2x - 1) - 2|)^2 - 1(-3|(2x - 1) - 2|) + 2) + 3) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1239 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(1π(2(-2(3|x - 3| - 2)^2 - 4(3|x - 3| - 2) + 4)^2 + 1(-2(3|x - 3| - 2)^2 - 4(3|x - 3| - 2) + 4) + 2) - 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 594 | MATH |
[
{
"content": "How many solutions does the equation 4(-4(5((-2x - 1)/(1x + 2))^2 + 4((-2x - 1)/(1x + 2)) - 2)^2 + 2(5((-2x - 1)/(1x + 2))^2 + 4((-2x - 1)/(1x + 2)) - 2) + 1)^2 + 2(-4(5((-2x - 1)/(1x + 2))^2 + 4((-2x - 1)/(1x + 2)) - 2)^2 + 2(5((-2x - 1)/(1x + 2))^2 + 4((-2x - 1)/(1x + 2)) - 2) + 1) - 5 = 0 have ... | 8 | MATH |
[
{
"content": "How many solutions does the equation 1cos(3π((-3(-1|(1x - 1) - 1| - 1) + 2)/(3(-1|(1x - 1) - 1| - 1) + 3)) + 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 44 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3(-3|((2(1x^2 - 5x - 2) + 3)/(1(1x^2 - 5x - 2) + 1)) - 3| + 2) + 2 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(-4((1(-2cos(2πx) - 3) + 1)/(-3(-2cos(2πx) - 3) + 1)) + 1) + 2)/(1(-4((1(-2cos(2πx) - 3) + 1)/(-3(-2cos(2πx) - 3) + 1)) + 1) - 3) 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) = (1((1(4(4x^2 - 3x - 1)^2 - 1(4x^2 - 3x - 1) - 4) - 3)/(-3(4(4x^2 - 3x - 1)^2 - 1(4x^2 - 3x - 1) - 4) + 2)) + 1)/(1((1(4(4x^2 - 3x - 1)^2 - 1(4x^2 - 3x - 1) - 4) - 3)/(-3(4(4x^2 - 3x - 1)^2 - 1(4x^2 - 3x - 1) - 4) + 2)) - 3) have in the interval [-10, 10]?\n\... | 4 | MATH |
[
{
"content": "How many solutions does the equation -3(2sin(3π(-1|(-2x^2 + 4x - 5) - 1|) + 1) - 1)^2 - 2(2sin(3π(-1|(-2x^2 + 4x - 5) - 1|) + 1) - 1) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1425 | MATH |
[
{
"content": "How many solutions does the equation 2(-2(1|(-1e^(-1x) + 1) + 1|) + 2)^2 - 2(-2(1|(-1e^(-1x) + 1) + 1|) + 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) = -5(1(-1sin(2π(3x^2 + 2x + 2) + 3) + 1)^2 + 4(-1sin(2π(3x^2 + 2x + 2) + 3) + 1) - 4) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1150 | MATH |
[
{
"content": "How many solutions does the equation -3sin(1π(3|((-3(-1x^2 - 5x - 1) + 2)/(-3(-1x^2 - 5x - 1))) + 3| + 1) + 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(-1|((-3(-1x^2 - 4x + 5) - 3)/(-3(-1x^2 - 4x + 5) + 2)) - 1| - 1)^2 + 2(-1|((-3(-1x^2 - 4x + 5) - 3)/(-3(-1x^2 - 4x + 5) + 2)) - 1| - 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 4 | MATH |
[
{
"content": "How many solutions does the equation 1cos(1π(2(-3|(2|x - 2| + 2) - 2| + 2) - 1) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "How many solutions does the equation -2sin(1π((3(-2|(4x^2 - 3x + 1) + 3| + 3) + 1)/(1(-2|(4x^2 - 3x + 1) + 3| + 3) + 3)) + 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "How many solutions does the equation 2cos(3π(3(-1|((2x + 3)/(3x - 1))| - 3) - 3) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 121 | MATH |
[
{
"content": "How many zeros does the function f(x) = 5((-2((-2(-3cos(2πx - 1) + 2) + 1)/(-1(-3cos(2πx - 1) + 2) + 3)) + 2)/(2((-2(-3cos(2πx - 1) + 2) + 1)/(-1(-3cos(2πx - 1) + 2) + 3)) + 3)) - 5 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) = -2|(-3(3(1x^2 + 4x + 5)^2 - 4(1x^2 + 4x + 5) - 1)^2 - 5(3(1x^2 + 4x + 5)^2 - 4(1x^2 + 4x + 5) - 1) + 2)| + 2 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) = 2cos(3π(2|(4(1x)^2 + 2(1x) - 3) + 2| + 1) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1634 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3(-4(-3sin(3π(1x - 3) - 2))^2 - 5(-3sin(3π(1x - 3) - 2)) + 3) - 5 where -10 ≤ x ≤ 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) = 2cos(2π((2((-3((-1x + 1)/(-1x + 2)) - 1)/(-3((-1x + 1)/(-1x + 2)))) + 3)/(-3((-3((-1x + 1)/(-1x + 2)) - 1)/(-3((-1x + 1)/(-1x + 2)))))) - 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 23 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(4(-2((1x + 3)/(-3x + 1))^2 + 1((1x + 3)/(-3x + 1)) + 1)^2 - 1(-2((1x + 3)/(-3x + 1))^2 + 1((1x + 3)/(-3x + 1)) + 1) - 2)^2 - 1(4(-2((1x + 3)/(-3x + 1))^2 + 1((1x + 3)/(-3x + 1)) + 1)^2 - 1(-2((1x + 3)/(-3x + 1))^2 + 1((1x + 3)/(-3x + 1))... | 5 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 4(-1sin(2π((3((-1x + 3)/(-2x - 3)))/(2((-1x + 3)/(-2x - 3)) - 1))) + 1)^2 - 1(-1sin(2π((3((-1x + 3)/(-2x - 3)))/(2((-1x + 3)/(-2x - 3)) - 1))) + 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 13 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2|(-1|(1(5x^2 - 3x)^2 - 3(5x^2 - 3x) - 1) - 1| + 3)| - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1|(3cos(2π((2(1|x + 3|) - 3)/(-3(1|x + 3|) - 1)) - 3) - 2) + 2| 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) = -5((-3(-5(3sin(2πx + 2) + 3)^2 + 4(3sin(2πx + 2) + 3) + 1) - 1)/(1(-5(3sin(2πx + 2) + 3)^2 + 4(3sin(2πx + 2) + 3) + 1) + 3)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many solutions does the equation -3sin(1π(1((1(-1|x - 3| + 2) + 3)/(-1(-1|x - 3| + 2) - 1))^2 - 2((1(-1|x - 3| + 2) + 3)/(-1(-1|x - 3| + 2) - 1)) - 5)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 226 | MATH |
[
{
"content": "How many zeros does the function f(x) = -5(1(-2cos(1π((-3x)/(3x - 2))))^2 + 4(-2cos(1π((-3x)/(3x - 2)))) - 4) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "How many solutions does the equation (1(2cos(2π((-2(2|x - 3| - 1) - 1)/(3(2|x - 3| - 1) + 1)) + 3) + 2) - 2)/(1(2cos(2π((-2(2|x - 3| - 1) - 1)/(3(2|x - 3| - 1) + 1)) + 3) + 2) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 17 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-5(5(1e^(1x)) - 1)^2 - 1(5(1e^(1x)) - 1) + 2)^2 - 3(-5(5(1e^(1x)) - 1)^2 - 1(5(1e^(1x)) - 1) + 2) - 1 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) = -1(3cos(1π(-1(5x^2 + 1)^2 + 5(5x^2 + 1) - 3) - 1) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 979 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2(-3(1(1x^2 + 5x + 1) - 2)^2 + 4(1(1x^2 + 5x + 1) - 2) + 5)^2 + 2(-3(1(1x^2 + 5x + 1) - 2)^2 + 4(1(1x^2 + 5x + 1) - 2) + 5) - 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(3|((3(2sin(1πx + 3)) - 3)/(3(2sin(1πx + 3)))) + 1| - 2)^2 - 2(3|((3(2sin(1πx + 3)) - 3)/(3(2sin(1πx + 3)))) + 1| - 2) - 5 = 0 have in the range [-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) = 4((-2(-3cos(3π(2x + 3) + 3)) + 1)/(-2(-3cos(3π(2x + 3) + 3)) - 3))^2 + 5((-2(-3cos(3π(2x + 3) + 3)) + 1)/(-2(-3cos(3π(2x + 3) + 3)) - 3)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 240 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1|((3(1sin(3π((-3x + 1)/(2x + 3)))) + 1)/(1(1sin(3π((-3x + 1)/(2x + 3)))) + 1)) + 2| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 71 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2cos(1π(3(-4(5x + 4)^2 - 4)^2 - 4(-4(5x + 4)^2 - 4) - 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 338 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1cos(3π(1|(-3(4x + 5)^2 + 1(4x + 5) + 3) + 3| - 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1574 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 4(3sin(3π((2(-3x - 4) - 2)/(1(-3x - 4)))) + 3)^2 + 1(3sin(3π((2(-3x - 4) - 2)/(1(-3x - 4)))) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2cos(1π(-3(-2|(1x + 3) - 3| + 2) + 1) + 2) + 2 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) = -3(1|(-3(-1x + 3)^2 + 3(-1x + 3) + 4) - 2| - 3)^2 - 3(1|(-3(-1x + 3)^2 + 3(-1x + 3) + 4) - 2| - 3) + 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1sin(1π(-4(-3(1|x - 2| + 3)) - 2) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many solutions does the equation -1(3sin(1π(5(-3|x - 3| + 1) + 3) + 3) + 1)^2 - 5(3sin(1π(5(-3|x - 3| + 1) + 3) + 3) + 1) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 298 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-2sin(3π(3((1x - 3)/(1x + 1))^2 + 4((1x - 3)/(1x + 1)) - 5) - 3) + 3)^2 - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 297 | MATH |
[
{
"content": "How many zeros does the function f(x) = -5(5(5(-1|x| + 1) + 3)^2 + 2(5(-1|x| + 1) + 3) - 3) - 3 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) = -2sin(3π(3|((-2(-1x + 2) - 1)/(1(-1x + 2) - 2))| + 2) - 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 137 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-3(1(3cos(2π((3x + 1)/(3x - 2)) - 2) - 3)^2 + 2(3cos(2π((3x + 1)/(3x - 2)) - 2) - 3) - 2) + 2)/(2(1(3cos(2π((3x + 1)/(3x - 2)) - 2) - 3)^2 + 2(3cos(2π((3x + 1)/(3x - 2)) - 2) - 3) - 2) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex f... | 14 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 5((-2(-2(-1x^2 - 4x + 5) - 1) - 3)/(2(-2(-1x^2 - 4x + 5) - 1) + 1))^2 - 2((-2(-2(-1x^2 - 4x + 5) - 1) - 3)/(2(-2(-1x^2 - 4x + 5) - 1) + 1)) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1|(-5((-3(-5x^2 + 5) + 1)/(-3(-5x^2 + 5)))^2 - 3((-3(-5x^2 + 5) + 1)/(-3(-5x^2 + 5))) + 5) + 2| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2cos(2π(5(-3|((-2x + 1)/(-2x - 3)) + 1| + 1)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 276 | MATH |
[
{
"content": "How many zeros does the function f(x) = -4((-1(1(-3cos(3πx) - 2)^2 - 2(-3cos(3πx) - 2) - 4) + 1)/(-2(1(-3cos(3πx) - 2)^2 - 2(-3cos(3πx) - 2) - 4) + 3)) + 3 have in the interval [-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) = -1cos(3π((-1(2(1x - 1) + 1) + 1)/(-2(2(1x - 1) + 1) + 3)) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -4(-4(3sin(3π(-3x^2 + 5x + 2) + 3) + 1) + 3)^2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1152 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(-2cos(3π(2(-3|x + 2|) - 4) - 2) - 2) + 1| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 173 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1((-3(2(-2x^2 - 5x + 1) + 3) - 3)/(2(2(-2x^2 - 5x + 1) + 3) + 1))^2 + 1((-3(2(-2x^2 - 5x + 1) + 3) - 3)/(2(2(-2x^2 - 5x + 1) + 3) + 1)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 4 | MATH |
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