messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1(-1|(-4(-1cos(1πx - 2) - 1)^2 - 4(-1cos(1πx - 2) - 1) - 4) + 3| + 3) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(2π(-2|(-3x^2 - 1x + 1) - 1| - 2) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1583 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3((3(-1cos(3π(4x - 5) + 1)) + 3)/(-2(-1cos(3π(4x - 5) + 1))))^2 + 2((3(-1cos(3π(4x - 5) + 1)) + 3)/(-2(-1cos(3π(4x - 5) + 1)))) - 3 have in the interval [-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) = -1|(-3sin(1π((1(-1x - 5) - 3)/(2(-1x - 5) + 2))) - 1) + 1| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 63 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2sin(3π(-1(3|x - 2| + 1) + 5)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "How many solutions does the equation -3cos(3π(-2|((-3(1x^2 - 5x + 2) - 2)/(2(1x^2 - 5x + 2) + 3)) - 2| + 1) + 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 98 | MATH |
[
{
"content": "How many zeros does the function f(x) = (2(-1cos(3π(1|(2x^2 + 5x - 5)|) - 2)) - 1)/(-3(-1cos(3π(1|(2x^2 + 5x - 5)|) - 2)) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1111 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2cos(3π(-3|(-1(-4x + 3)^2 + 4(-4x + 3))| + 2) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1606 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1(3(1sin(1πx - 2) + 1) - 2)^2 + 2(3(1sin(1πx - 2) + 1) - 2) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3sin(2π(-5(1|x| + 3)^2 - 2(1|x| + 3) - 1) - 2) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1259 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1(1|(-3cos(2π(-3x - 2) + 1)) - 3| + 3)^2 - 5(1|(-3cos(2π(-3x - 2) + 1)) - 3| + 3) - 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 1sin(1π(1(1(-2|x + 3|)^2 - 5(-2|x + 3|) + 5)) + 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 481 | MATH |
[
{
"content": "How many zeros does the function f(x) = 5(-3cos(3π(5x^2 + 1x - 2) - 1)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1591 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2cos(3π(-2|(5x + 2) - 3| + 2) + 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 600 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(3sin(3π(3|x + 1| - 3)) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 182 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(2π(-3((2(3|x + 2| - 2) - 2)/(-1(3|x + 2| - 2) + 2)) + 3) - 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 1(-2|(2cos(3πx + 1)) + 1|)^2 - 2(-2|(2cos(3πx + 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) = -2(-1sin(1π(1|x + 2| - 1) + 2) - 2) - 4 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) = 2sin(2π(-1|(-1((-3x + 3)/(2x + 2))^2 - 4((-3x + 3)/(2x + 2)) + 2) + 3|)) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 171 | MATH |
[
{
"content": "How many zeros does the function f(x) = (3(1(-2sin(2πx) - 1)^2 - 4(-2sin(2πx) - 1)) - 3)/(-1(1(-2sin(2πx) - 1)^2 - 4(-2sin(2πx) - 1)) - 2) 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 1(2sin(3π(2|(-3x + 3) + 1| + 2) - 1) - 2)^2 + 4(2sin(3π(2|(-3x + 3) + 1| + 2) - 1) - 2) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 337 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -5(-1sin(2π(2|((-2x + 2)/(2x - 3)) + 2| - 1) + 1) + 1) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3sin(2π(-3|((1(-3x^2 + 2x - 2) + 2)/(3(-3x^2 + 2x - 2) + 3)) + 1|) + 3) + 2 have in the interval [-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) = -1sin(2π(-2((1x - 2)/(-2x + 3))^2 - 3) + 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(2(-3sin(2πx - 2) + 1)^2 - 4(-3sin(2πx - 2) + 1) - 4) - 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) = -3|((-1(3sin(1π(-1x + 4) - 3) + 1) + 3)/(-1(3sin(1π(-1x + 4) - 3) + 1) - 2)) + 1| + 3 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|(3cos(2π(3(-1x^2 - 4)) + 1) - 1)| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 439 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(2π(-1(3(-3|x - 3| - 1) - 2)^2 + 1(3(-3|x - 3| - 1) - 2) - 5) + 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1280 | MATH |
[
{
"content": "How many zeros does the function f(x) = (3(-3(3sin(1π(-2|x + 1| + 3)) + 3)^2 + 3(3sin(1π(-2|x + 1| + 3)) + 3) + 2) + 3)/(-2(-3(3sin(1π(-2|x + 1| + 3)) + 3)^2 + 3(3sin(1π(-2|x + 1| + 3)) + 3) + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 40 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2cos(3π(-2|(-1(-1x - 3)^2 + 5(-1x - 3) + 2) - 1| + 1)) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 649 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(1π(4(3|(-4x^2 + 4x + 3) - 2| + 3) - 5) + 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1272 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(1π(-4(-3|x + 1| - 1)^2 + 1(-3|x + 1| - 1))) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1530 | MATH |
[
{
"content": "How many solutions does the equation -3sin(2π(4((2(1|x - 3| - 3) - 3)/(-1(1|x - 3| - 3) + 3)) - 3) - 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 186 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1sin(1π(1|(-4((3x)/(2x - 3))^2 + 1((3x)/(2x - 3)) + 3) - 3| + 2) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 196 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3(3cos(3π(2|x| - 1) + 3) - 1) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many solutions does the equation -3|(1sin(2π(4x) + 2) + 1) - 2| + 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) = 2|(-1cos(2π((1(-4x^2 - 2x + 3) + 3)/(2(-4x^2 - 2x + 3) + 3))) + 2) - 2| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "How many solutions does the equation (-2(3cos(2π(-1x^2 + 1x - 4) - 2) + 3) + 3)/(-1(3cos(2π(-1x^2 + 1x - 4) - 2) + 3) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 229 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1((1(-3sin(2πx + 1)))/(-3(-3sin(2πx + 1)) + 2))^2 + 4((1(-3sin(2πx + 1)))/(-3(-3sin(2πx + 1)) + 2)) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1(-2(-3sin(1π(4x^2 + 3x - 3) - 1) - 3) - 3) + 2)/(3(-2(-3sin(1π(4x^2 + 3x - 3) - 1) - 3) - 3)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 550 | MATH |
[
{
"content": "How many solutions does the equation 2sin(1π(5(-3|((1x - 2)/(-1x)) + 3| - 3)^2 - 1(-3|((1x - 2)/(-1x)) + 3| - 3) - 4) - 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 716 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1cos(3π(1|((-3x)/(2x - 1)) + 3| - 2) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2cos(2π((-3(-1(-4x - 5)^2 + 2(-4x - 5) + 4) + 3)/(-2(-1(-4x - 5)^2 + 2(-4x - 5) + 4) - 1)) - 2) - 2 have in the interval [-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) = 3cos(2π(-1(-3x - 4)^2 - 5(-3x - 4) - 4) - 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1325 | MATH |
[
{
"content": "How many solutions does the equation 1cos(3π(2((-2x)/(1x - 2))^2 + 5((-2x)/(1x - 2)) + 5) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 213 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-2(3(1|(-3cos(2πx - 3)) - 3| - 2) + 4) - 2)/(1(3(1|(-3cos(2πx - 3)) - 3| - 2) + 4)) 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 3sin(1π((-1(-2(2x^2) + 1) + 1)/(-1(-2(2x^2) + 1) - 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 solutions does the equation 2sin(3π(1(1|x - 2| + 1)^2 - 3(1|x - 2| + 1) + 4) + 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 564 | MATH |
[
{
"content": "How many solutions does the equation 4(3((1(-3sin(1πx - 1) + 1) - 2)/(2(-3sin(1πx - 1) + 1))) - 4)^2 + 2(3((1(-3sin(1πx - 1) + 1) - 2)/(2(-3sin(1πx - 1) + 1))) - 4) - 2 = 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 (3(-3sin(3π(-2|x + 2| + 3) - 1) + 2) - 1)/(-2(-3sin(3π(-2|x + 2| + 3) - 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": "Determine the number of values x in [-10, 10] where f(x) = 4(5((-2(-2sin(3πx + 1)) + 1)/(3(-2sin(3πx + 1)) + 2))^2 + 3((-2(-2sin(3πx + 1)) + 1)/(3(-2sin(3πx + 1)) + 2)) - 2) + 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|(3cos(3π((2x - 2)/(-3x - 3)) + 2) + 3)| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 66 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(3π(-5(-1x^2 + 3x) + 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1651 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3(-1(-1sin(1πx + 2) + 3)^2 + 1(-1sin(1πx + 2) + 3) + 4) + 5 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) = -2|((-1(-1(-2sin(3πx) - 1) - 3) - 1)/(-2(-1(-2sin(3πx) - 1) - 3)))| have in the interval [-10, 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) = (1(-3|(3cos(1π(-5x + 1) + 3)) - 2| + 2))/(-3(-3|(3cos(1π(-5x + 1) + 3)) - 2| + 2) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 166 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1(-2|(-1cos(1π(5x^2 - 5x + 2) - 2) - 1) - 2| + 1) + 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 942 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3|(1cos(1π(2(-1x^2 + 5x + 2) - 5) + 1) + 2) - 2| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 849 | MATH |
[
{
"content": "How many solutions does the equation -1((-2(2e^(2(-5x)) - 1) + 2)/(1(2e^(2(-5x)) - 1) - 3))^2 - 2((-2(2e^(2(-5x)) - 1) + 2)/(1(2e^(2(-5x)) - 1) - 3)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-4(-2sin(2π((-3x - 1)/(-2x - 1)) - 3) + 1) - 3)^2 + 4(-4(-2sin(2π((-3x - 1)/(-2x - 1)) - 3) + 1) - 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "How many solutions does the equation 2sin(2π(-2|((-3x + 1)/(-1x - 1)) - 2| - 3) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 130 | MATH |
[
{
"content": "How many solutions does the equation -1(-3|(-1sin(3πx + 2)) + 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 -3(-1sin(1π((-1(3|x + 1| - 2) - 3)/(1(3|x + 1| - 2) + 1)) - 1) - 1)^2 - 1(-1sin(1π((-1(3|x + 1| - 2) - 3)/(1(3|x + 1| - 2) + 1)) - 1) - 1) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 53 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (3(3sin(1π(-5x^2 + 2x - 1) + 2) - 2) + 1)/(1(3sin(1π(-5x^2 + 2x - 1) + 2) - 2) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 927 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(2cos(3π(3x + 5))) - 3)/(-2(2cos(3π(3x + 5))) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3sin(3π(5(1x^2 + 2x - 3))) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1645 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2(-1|(1cos(2π((-2x - 2)/(3x - 2)) - 3) + 3) - 1| + 3)^2 + 1(-1|(1cos(2π((-2x - 2)/(3x - 2)) - 3) + 3) - 1| + 3) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-1(2cos(3πx - 2) + 2) + 4)^2 - 3(-1(2cos(3πx - 2) + 2) + 4) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many solutions does the equation 2|((2(-1cos(3πx - 3)) + 3)/(1(-1cos(3πx - 3)))) + 3| = 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) = 2cos(2π(3((1x - 3)/(2x + 1))^2 - 2) + 3) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 167 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2|((2(2(2sin(1πx)) + 2) + 2)/(2(2(2sin(1πx)) + 2))) - 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1sin(1π((-1(-1|x - 1| - 1) - 3)/(-3(-1|x - 1| - 1) - 3)) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "How many solutions does the equation -2sin(1π((1(1x + 2) + 2)/(-3(1x + 2) - 2)) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(2π(1((3(-2x^2 + 1x + 4) + 1)/(2(-2x^2 + 1x + 4) + 3)) + 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 53 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(3π(1|(5x + 2) - 1| + 2) - 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 300 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3sin(3π(2|(-4((-3x + 2)/(2x - 1)) + 2) - 2| + 3) + 1) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 73 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-2|(-2sin(1π(5x^2 + 5x - 1) + 1) + 3)| + 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 439 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 4(5(1cos(2πx + 3))^2 + 5(1cos(2πx + 3)) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2cos(2π(4((-3(-5x^2 + 3x) + 2)/(-1(-5x^2 + 3x))) - 4)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 96 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -5(-3sin(2π(-3x^2 + 5x - 3) - 1) - 2) + 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 513 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1(3|(3cos(1πx - 2) + 2) - 3| + 1) - 1)/(1(3|(3cos(1πx - 2) + 2) - 3| + 1) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2|((2(-5(3sin(3πx + 3) + 1) - 1) + 1)/(3(-5(3sin(3πx + 3) + 1) - 1) - 2)) - 2| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1((-2(2cos(3π(-5x - 5) - 2) - 1) - 2)/(-2(2cos(3π(-5x - 5) - 2) - 1) + 1))^2 - 4((-2(2cos(3π(-5x - 5) - 2) - 1) - 2)/(-2(2cos(3π(-5x - 5) - 2) - 1) + 1)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 600 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2sin(2π((2(-3x^2 - 1x + 2))/(-1(-3x^2 - 1x + 2) - 1)) + 1) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1((1(-2(-2sin(2πx + 1) + 1)^2 + 4(-2sin(2πx + 1) + 1) + 4) - 1)/(-3(-2(-2sin(2πx + 1) + 1)^2 + 4(-2sin(2πx + 1) + 1) + 4))) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(1π(5(2((1x - 2)/(-2x + 1)) - 4)^2 - 4(2((1x - 2)/(-2x + 1)) - 4) - 5) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 178 | MATH |
[
{
"content": "How many solutions does the equation 3sin(2π(-3|(-2x) - 3| - 1)) + 2 = 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) = 3sin(1π(5(2(-3|x - 3|)^2 - 2) - 2) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1279 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-1(-2sin(3π(5x + 2) - 1)) + 2)/(1(-2sin(3π(5x + 2) - 1))) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 150 | MATH |
[
{
"content": "How many solutions does the equation (-2(-4(1(1sin(3πx) - 2) + 3)^2 - 2(1(1sin(3πx) - 2) + 3) + 1))/(3(-4(1(1sin(3πx) - 2) + 3)^2 - 2(1(1sin(3πx) - 2) + 3) + 1) + 1) = 0 have in the range [-10, 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) = -4(-3cos(1π(2(-3|x - 2| - 3)^2 + 5(-3|x - 2| - 3) - 4) + 1) - 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 754 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2(-3|(-2sin(1π((-3x - 3)/(-1x + 3)) + 2) + 2) - 2|)^2 + 3(-3|(-2sin(1π((-3x - 3)/(-1x + 3)) + 2) + 2) - 2|) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2((1(-4(1sin(1πx - 3)) - 1) + 3)/(3(-4(1sin(1πx - 3)) - 1) + 3))^2 - 1((1(-4(1sin(1πx - 3)) - 1) + 3)/(3(-4(1sin(1πx - 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": "Find the number of x-intercepts of the function f(x) = (-2(-1(-3cos(3πx - 2))^2 + 3(-3cos(3πx - 2)) + 1))/(-3(-1(-3cos(3πx - 2))^2 + 3(-3cos(3πx - 2)) + 1) + 4) 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) = 2cos(1π((-2(-3|x + 1| + 1) + 2)/(-2(-3|x + 1| + 1) - 3)) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 64 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-1(-2cos(2π(3x + 4) - 2) - 3) - 1)/(2(-2cos(2π(3x + 4) - 2) - 3) - 1) have in the interval [-10, 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) = -1|(-3sin(1π((1(5x - 3) + 3)/(-2(5x - 3) + 3))) - 1) + 1| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(5(2cos(1π(2x^2 - 5x - 3) - 2)) + 3) + 2)/(3(5(2cos(1π(2x^2 - 5x - 3) - 2)) + 3) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 275 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3|((-3(-1(2sin(2πx + 2) + 2)^2 - 3(2sin(2πx + 2) + 2)))/(-1(-1(2sin(2πx + 2) + 2)^2 - 3(2sin(2πx + 2) + 2)) + 2)) - 1| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many solutions does the equation -1(-1sin(2π((3(-4x + 2) - 2)/(2(-4x + 2))) - 3) + 1)^2 - 3(-1sin(2π((3(-4x + 2) - 2)/(2(-4x + 2))) - 3) + 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
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