messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "How many solutions does the equation -4(1(2cos(2π(-3|x - 1|) - 2) + 2)^2 - 4) - 5 = 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 (1(-2sin(2π(5x^2 + 4x - 3) - 3) + 1) - 3)/(-1(-2sin(2π(5x^2 + 4x - 3) - 3) + 1)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 980 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1cos(1π((-1(-1x^2 - 2x - 1) + 2)/(-2(-1x^2 - 2x - 1) - 3)) - 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1(2cos(1π(-1x^2 + 2x + 5) + 1) + 1) - 1)/(-2(2cos(1π(-1x^2 + 2x + 5) + 1) + 1) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 201 | MATH |
[
{
"content": "How many solutions does the equation (2(3|(-1(-3sin(2πx - 3) - 1) + 2)| - 2) - 2)/(-3(3|(-1(-3sin(2πx - 3) - 1) + 2)| - 2)) = 0 have in the range [-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) = 1sin(3π(2(2x - 1)^2 - 1(2x - 1) + 2)) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1095 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 4(-2cos(1π(5((-1x - 1)/(-3x + 4))^2 - 1((-1x - 1)/(-3x + 4)) - 1) - 1) + 3) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | MATH |
[
{
"content": "How many solutions does the equation (-2(-3|(-1sin(1πx) + 2) - 3|) - 2)/(3(-3|(-1sin(1πx) + 2) - 3|) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -4(2cos(3π(-5(-1|x + 2| + 3)^2 + 3) + 3) - 2) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1144 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3((1(1sin(2π(2|x - 1| - 3) - 1) - 1) - 2)/(1(1sin(2π(2|x - 1| - 3) - 1) - 1) + 2)) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(1π(-3|((2x + 2)/(2x - 1)) + 1| + 2) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 77 | MATH |
[
{
"content": "How many solutions does the equation -2sin(2π(2((3(1|x|) - 3)/(1(1|x|) + 1)) + 5) - 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 44 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(-3sin(1π((-3x + 1)/(-2x - 3)) - 2) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2cos(1π(2|(-1x^2 + 4x - 3) + 3|) + 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 416 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (3(3sin(3π(4x^2 - 5x + 4) - 3) + 3) - 1)/(2(3sin(3π(4x^2 - 5x + 4) - 3) + 3) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 825 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2cos(1π(-1|(-3((-1x + 2)/(1x - 3))^2 + 2((-1x + 2)/(1x - 3))) - 3| - 1) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 98 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1cos(3π(4(-2x^2 + 1x - 5)) + 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1077 | MATH |
[
{
"content": "How many solutions does the equation (-1(-3cos(3π(2x - 2) - 1) + 1))/(3(-3cos(3π(2x - 2) - 1) + 1) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -4(-3|(2cos(3πx - 3) - 1) + 3| + 2) + 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2((2(3sin(2πx - 2)))/(2(3sin(2πx - 2)) - 1))^2 + 3((2(3sin(2πx - 2)))/(2(3sin(2πx - 2)) - 1)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many solutions does the equation 2sin(1π(-1|((-2(-1x - 1) - 3)/(-1(-1x - 1) + 3))|)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 107 | MATH |
[
{
"content": "How many solutions does the equation -2(3cos(2π((-1(1|x| - 1) + 1)/(-2(1|x| - 1) - 3))) - 1) - 3 = 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 -2sin(2π(5(3((2x + 3)/(-3x - 3)) - 2)^2 - 1(3((2x + 3)/(-3x - 3)) - 2) + 4) - 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "How many solutions does the equation -3sin(2π((-3(-2|x + 3| - 2) + 3)/(-2(-2|x + 3| - 2) - 2)) - 2) + 2 = 0 have in the range [-10, 10]?\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) = -1((3(-2sin(3πx + 2) - 3) - 3)/(2(-2sin(3πx + 2) - 3) + 3))^2 + 3((3(-2sin(3πx + 2) - 3) - 3)/(2(-2sin(3πx + 2) - 3) + 3)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many solutions does the equation (-2(-1cos(1π(3|x + 2|) + 2) - 1) - 1)/(-2(-1cos(1π(3|x + 2|) + 2) - 1) + 3) = 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 3((-3(-2cos(2π(-1|x + 2| + 3))) + 1)/(3(-2cos(2π(-1|x + 2| + 3))))) - 2 = 0 have in the range [-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) = -2sin(1π(2(-1|x - 1| - 1)^2 + 5) + 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 230 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3(-3|(-1sin(2π(3x + 2) + 3)) - 2| + 3)^2 - 4(-3|(-1sin(2π(3x + 2) + 3)) - 2| + 3) + 2 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) = (-3(2|(2(-1sin(2πx - 3) + 2)^2 - 4) + 2| - 3) - 3)/(-1(2|(2(-1sin(2πx - 3) + 2)^2 - 4) + 2| - 3) - 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 2cos(3π(4(3x^2 - 3x - 2) - 2)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1062 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-2(-2|(4(-2cos(1πx - 3) + 2) - 3) - 2| - 1) - 2)/(-2(-2|(4(-2cos(1πx - 3) + 2) - 3) - 2| - 1) + 3) where -10 ≤ x ≤ 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) = -3|(2sin(1π(4(-3x^2 - 1x + 2) - 2) - 3)) + 1| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 676 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1cos(1π(-1|(-3x + 4) - 1| + 2) + 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "How many solutions does the equation 3(3|(-3sin(3πx + 2) + 3) - 1| - 2)^2 + 3(3|(-3sin(3πx + 2) + 3) - 1| - 2) - 2 = 0 have in the range [-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) = -4(1|(-2sin(2π((-3x - 3)/(-1x - 3)) - 2) + 2) - 2|) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 93 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2cos(1π(2(-1|x - 2| - 2) - 3) + 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 solutions does the equation -3cos(2π(2|((-3(-1x - 4) + 1)/(-2(-1x - 4) - 1)) - 1| - 2) - 2) + 3 = 0 have in the range [-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) = -1(-3cos(3π(1|((1x + 2)/(-1x + 2)) + 1| + 1) + 3) + 2) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 117 | MATH |
[
{
"content": "How many solutions does the equation (2(3cos(1π(1|(-2x - 2) - 2| - 3)) + 1) + 2)/(-1(3cos(1π(1|(-2x - 2) - 2| - 3)) + 1) + 3) = 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) = 5((-2(1|(-2sin(1πx - 2) - 1) - 3| - 1) + 2)/(2(1|(-2sin(1πx - 2) - 1) - 3| - 1) - 1)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3π(1((2(4x - 3))/(-1(4x - 3) + 3))^2 - 5((2(4x - 3))/(-1(4x - 3) + 3)) - 4) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 206 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1cos(2π(-4(-1x^2 - 2x - 4) + 4) - 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 684 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(1π(2|(-3(-1x^2 + 4x - 2) + 5) + 1| + 3) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1167 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-1(-5(-3cos(1πx + 1) - 1)^2 + 5(-3cos(1πx + 1) - 1) + 3) + 3)/(1(-5(-3cos(1πx + 1) - 1)^2 + 5(-3cos(1πx + 1) - 1) + 3)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3|((-1(-4(-3cos(2πx - 2) + 2)^2 - 5(-3cos(2πx - 2) + 2) - 5) + 2)/(-1(-4(-3cos(2πx - 2) + 2)^2 - 5(-3cos(2πx - 2) + 2) - 5) - 3)) - 3| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "How many solutions does the equation -2sin(3π(-2((1x - 2)/(2x - 1))^2 + 3) - 1) - 2 = 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|(-1(-2sin(3πx + 1) + 3)^2 + 3(-2sin(3πx + 1) + 3) + 3) + 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) = 5(3sin(1π((1(-1x + 2))/(3(-1x + 2) - 2)) + 2) + 1)^2 + 2(3sin(1π((1(-1x + 2))/(3(-1x + 2) - 2)) + 2) + 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3|(-1(-2sin(1π((2x + 3)/(2x - 3))) + 3)^2 + 5(-2sin(1π((2x + 3)/(2x - 3))) + 3) - 3) + 2| where -10 ≤ x ≤ 10.\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) = 2|(-1cos(2π(-5(3x^2 + 1x - 5) + 1)) + 2) - 3| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1475 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-1(1(-3cos(2πx - 1))^2 + 1(-3cos(2πx - 1)) - 1)) - 3)/(1(-1(1(-3cos(2πx - 1))^2 + 1(-3cos(2πx - 1)) - 1))) 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(-3cos(2π((3x + 3)/(3x + 1))) + 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 44 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 5(1(3cos(3πx) - 1)^2 - 4(3cos(3πx) - 1) + 2) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 5(1sin(3π((-3x)/(-1x + 2)) + 1) - 1)^2 - 4(1sin(3π((-3x)/(-1x + 2)) + 1) - 1) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 145 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2sin(3π((-2(-1x - 3) + 3)/(2(-1x - 3) + 1)) + 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 86 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2cos(2π((-1(-1x^2 + 5x - 4) - 3)/(-1(-1x^2 + 5x - 4) + 2)) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 170 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3sin(3π(3|((1x - 3)/(2x - 3)) - 1| - 3) + 3) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 75 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(3π(1(-3((-3x + 1)/(3x - 2)))^2 - 5(-3((-3x + 1)/(3x - 2))) + 4) + 2) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | MATH |
[
{
"content": "How many zeros does the function f(x) = (3(-4(3sin(2πx - 1) - 1) + 3) + 1)/(-3(-4(3sin(2πx - 1) - 1) + 3) + 2) 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) = -3sin(3π(5((-2(-3|x + 2| - 1) - 3)/(2(-3|x + 2| - 1))) - 4) - 2) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1|(3cos(2π(-2x^2 + 2x - 5) + 1) - 3)| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 800 | MATH |
[
{
"content": "How many zeros does the function f(x) = -5(3cos(3π((-1x + 2)/(-1x - 1)) - 2) - 2)^2 + 3(3cos(3π((-1x + 2)/(-1x - 1)) - 2) - 2) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 103 | MATH |
[
{
"content": "How many solutions does the equation -2cos(2π((2(1(2x^2 - 5x) + 3) - 1)/(-2(1(2x^2 - 5x) + 3))) + 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 5(1sin(1π(-4x^2 + 2x + 4) + 3) - 1) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 796 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-1sin(1π(-2|x - 1| - 2) + 2) + 1) - 3)/(-2(-1sin(1π(-2|x - 1| - 2) + 2) + 1) - 3) 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) = 1((1(-3sin(3πx + 1) + 1) + 1)/(2(-3sin(3πx + 1) + 1) - 1))^2 - 4((1(-3sin(3πx + 1) + 1) + 1)/(2(-3sin(3πx + 1) + 1) - 1)) - 5 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 (1(-2|(-2cos(2π(-1x^2 - 4x + 3) - 2) + 1) - 1|))/(1(-2|(-2cos(2π(-1x^2 - 4x + 3) - 2) + 1) - 1|) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 382 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(2cos(3π(-3|x + 1| - 1) - 3) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 89 | MATH |
[
{
"content": "How many solutions does the equation -1sin(2π(-1|(4x - 2) + 1| - 3) - 2) + 1 = 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 -1(-3cos(1π(1((2x - 1)/(-2x - 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"
}
] | 48 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-3(3sin(1π(1|x| + 3) + 1)) + 3)/(-3(3sin(1π(1|x| + 3) + 1)) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many zeros does the function f(x) = (3(-3cos(1π(-5(4x - 5)^2 + 4(4x - 5) - 4)) - 1) + 1)/(3(-3cos(1π(-5(4x - 5)^2 + 4(4x - 5) - 4)) - 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 213 | MATH |
[
{
"content": "How many solutions does the equation -5(-3|((2(3cos(2πx - 2) + 2) - 3)/(-1(3cos(2πx - 2) + 2)))| + 3) + 2 = 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) = -5(3(-2cos(1π(-3|x + 2| - 1)) - 3) + 3)^2 - 4(3(-2cos(1π(-3|x + 2| - 1)) - 3) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many solutions does the equation 3cos(2π(5(-1|((-3x - 1)/(-2x - 1))| + 1) + 5) - 2) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2cos(1π(1(-1((3x - 1)/(1x - 2))^2 + 1((3x - 1)/(1x - 2)) + 4) + 4) - 2) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 126 | MATH |
[
{
"content": "How many solutions does the equation -2sin(1π(2((2(1x) - 3)/(1(1x) + 1))^2 + 2((2(1x) - 3)/(1(1x) + 1))) - 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 171 | MATH |
[
{
"content": "How many solutions does the equation -4((-2(4(2cos(1πx + 1) + 2) - 1) - 2)/(3(4(2cos(1πx + 1) + 2) - 1) - 2))^2 + 5((-2(4(2cos(1πx + 1) + 2) - 1) - 2)/(3(4(2cos(1πx + 1) + 2) - 1) - 2)) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 20 | MATH |
[
{
"content": "How many solutions does the equation (-1(2|(4(-2cos(3πx + 1) - 1)^2 - 5) + 1| - 3) - 2)/(-3(2|(4(-2cos(3πx + 1) - 1)^2 - 5) + 1| - 3) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3(3(-2sin(2π((2x + 3)/(-2x - 1)) + 3) - 3) + 3)^2 - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2|((2(1cos(3π(-2x + 2) + 2) - 1) - 3)/(1(1cos(3π(-2x + 2) + 2) - 1) + 1)) + 2| + 3 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) = -1sin(2π(-5(3|x - 3| + 1) + 5) - 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 296 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2cos(3π(2|(4x^2 - 4) - 2| + 1) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1453 | MATH |
[
{
"content": "How many solutions does the equation (2(-3sin(1π(5x^2 + 4x + 5) - 1) + 2))/(-3(-3sin(1π(5x^2 + 4x + 5) - 1) + 2) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 428 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3(2(-1sin(3π(-3|x - 1| + 2) - 3) + 2)^2 - 5(-1sin(3π(-3|x - 1| + 2) - 3) + 2) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 75 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3cos(2π(1(3|x + 3| - 3)^2 - 2(3|x + 3| - 3) - 2) - 3) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1426 | MATH |
[
{
"content": "How many solutions does the equation 3cos(3π(-1(-2|((-2x + 3)/(-3x))| + 2) + 4)) + 2 = 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) = 3sin(1π(3((1x + 2)/(1x - 3))^2 - 4((1x + 2)/(1x - 3)) + 1) + 1) + 2 equals zero.\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((-3(4x^2 - 1x + 4))/(-1(4x^2 - 1x + 4) + 2)) - 3) + 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1|((-2(2sin(2π(-2x + 3)) + 1))/(3(2sin(2π(-2x + 3)) + 1) - 1)) + 3| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 155 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3π(2|(5((1x + 1)/(1x - 3)) - 5) + 2| - 1) - 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 224 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3sin(2π(1|((-3(4x^2 - 2x + 1) - 2)/(1(4x^2 - 2x + 1) - 3)) + 1| - 1) + 2) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 113 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(2π((1(-1|x + 2| + 2) + 1)/(-1(-1|x + 2| + 2) + 2)) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 89 | MATH |
[
{
"content": "How many solutions does the equation 3cos(3π(4(-4((-2x + 1)/(-3x - 2)) - 1)^2 - 5(-4((-2x + 1)/(-3x - 2)) - 1) + 4) - 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 499 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2|(-2sin(2π((3x + 1)/(2x + 1)) + 3) + 2) - 3| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(-1(-3cos(2π((-1x + 2)/(-3x - 2)) - 2) - 2)^2 - 4(-3cos(2π((-1x + 2)/(-3x - 2)) - 2) - 2)) + 3| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68 | MATH |
[
{
"content": "How many solutions does the equation 5(2sin(2π(-4x^2 + 4x - 3) + 2) + 1) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 682 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1sin(1π((2(2|x| - 1) - 1)/(-3(2|x| - 1) - 3)) - 1) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "How many solutions does the equation -1(2sin(2π(3((-3x - 3)/(-1x + 3)) - 4) + 2) - 1)^2 + 2(2sin(2π(3((-3x - 3)/(-1x + 3)) - 4) + 2) - 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 294 | MATH |
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