messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "How many solutions does the equation 1sin(1π(-2((3(-1|x| + 2))/(-1(-1|x| + 2) - 3)) - 5) + 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 178 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3sin(1π(5(-3|(-1|x - 2| - 3) - 1| + 3) + 2) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 300 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2((-2(-5(-2cos(2πx + 3) - 1)^2 - 5(-2cos(2πx + 3) - 1) + 1) - 1)/(-1(-5(-2cos(2πx + 3) - 1)^2 - 5(-2cos(2πx + 3) - 1) + 1) + 2)))/(-2((-2(-5(-2cos(2πx + 3) - 1)^2 - 5(-2cos(2πx + 3) - 1) + 1) - 1)/(-1(-5(-2cos(2πx + 3) - 1)^2 - 5(-2cos(2... | 80 | MATH |
[
{
"content": "How many solutions does the equation (-1(3cos(2π(3(1x^2 + 3x + 4) + 4) + 1)) - 1)/(2(3cos(2π(3(1x^2 + 3x + 4) + 4) + 1)) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 732 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 5((-1(4(3sin(2πx + 1) + 2)^2 + 1(3sin(2πx + 1) + 2) - 2) + 1)/(-1(4(3sin(2πx + 1) + 2)^2 + 1(3sin(2πx + 1) + 2) - 2) + 2))^2 + 2((-1(4(3sin(2πx + 1) + 2)^2 + 1(3sin(2πx + 1) + 2) - 2) + 1)/(-1(4(3sin(2πx + 1) + 2)^2 + 1(3sin(2πx + 1) + 2) ... | 40 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(1π(-2(-2|(1x^2 + 4x - 4) + 2| - 3) - 5) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 832 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 4(-3((-1(-2|x + 1| + 2) - 2)/(-3(-2|x + 1| + 2) - 3)) - 2)^2 + 3(-3((-1(-2|x + 1| + 2) - 2)/(-3(-2|x + 1| + 2) - 3)) - 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) = 3((3((-2(-2cos(2πx + 3)) + 3)/(-2(-2cos(2πx + 3)) - 2)) + 1)/(-2((-2(-2cos(2πx + 3)) + 3)/(-2(-2cos(2πx + 3)) - 2)) + 3)) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(3|(-3sin(3π(1|x + 1| + 2) + 1) + 3) - 3| + 3) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2(1(3sin(3π((-2x + 1)/(1x + 2)) + 2) - 3) + 2)^2 + 1(1(3sin(3π((-2x + 1)/(1x + 2)) + 2) - 3) + 2) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 188 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1cos(2π((3(4(-1x + 3)^2 - 5(-1x + 3) - 5) + 1)/(-2(4(-1x + 3)^2 - 5(-1x + 3) - 5) - 1)) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "How many solutions does the equation -1((1(3sin(3π(1x^2 - 1x + 5) + 1) - 2) + 1)/(2(3sin(3π(1x^2 - 1x + 5) + 1) - 2))) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 93 | MATH |
[
{
"content": "How many solutions does the equation -2|((-2(4((1x - 1)/(-2x - 2))^2 + 5((1x - 1)/(-2x - 2)) - 1) + 2)/(3(4((1x - 1)/(-2x - 2))^2 + 5((1x - 1)/(-2x - 2)) - 1) - 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": "How many zeros does the function f(x) = -3cos(3π(-4(-4(2x^2 + 4) + 2)^2 - 5(-4(2x^2 + 4) + 2)) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 402 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1cos(1π((3(-2(4x + 2)^2 - 1(4x + 2) - 1) + 1)/(-2(-2(4x + 2)^2 - 1(4x + 2) - 1) - 3))) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(2π(2|((2((-2x + 3)/(3x - 2)) - 2)/(-2((-2x + 3)/(3x - 2)) + 3)) - 1| + 1) - 3) + 1 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) = 4(-3|(-2(1sin(3πx - 2) - 1)^2 + 2(1sin(3πx - 2) - 1) + 3) + 3| + 1)^2 - 4(-3|(-2(1sin(3πx - 2) - 1)^2 + 2(1sin(3πx - 2) - 1) + 3) + 3| + 1) 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) = -1sin(1π(-2|(-1((2x + 1)/(3x + 2))^2 - 4((2x + 1)/(3x + 2)) + 4) + 2| - 1) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2|(-2cos(2π(4(-3|x + 3| + 1)^2 - 5(-3|x + 3| + 1) - 5)) + 1) - 2| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 79 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2cos(2π(-1|(-5((-1x - 3)/(-2x + 3))^2 - 5((-1x - 3)/(-2x + 3)) + 4) - 3| + 3) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 269 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1|(-2|(1(2x - 3)^2 + 4(2x - 3) - 5) - 2| - 2) + 1| - 3 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) = 1sin(2π(-1((1(-1x^2 - 3x + 1))/(3(-1x^2 - 3x + 1) + 2))^2 + 4((1(-1x^2 - 3x + 1))/(3(-1x^2 - 3x + 1) + 2)) + 3) + 1) 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) = 1sin(1π(4(1((-2x + 3)/(-1x + 2))^2 + 2((-2x + 3)/(-1x + 2)) - 2) - 4) - 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 92 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(3π(-1|(3|(-5x + 4) - 3| - 3) - 3| - 2)) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 414 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1((2((-3(-3sin(2πx - 3) - 2) + 2)/(-1(-3sin(2πx - 3) - 2) + 2)) - 1)/(-3((-3(-3sin(2πx - 3) - 2) + 2)/(-1(-3sin(2πx - 3) - 2) + 2))))^2 + 1((2((-3(-3sin(2πx - 3) - 2) + 2)/(-1(-3sin(2πx - 3) - 2) + 2)) - 1)/(-3((-3(-3sin(2πx - 3) - 2) + 2)/(-1... | 60 | MATH |
[
{
"content": "How many solutions does the equation 2cos(3π(-5(-2|(2x + 5)|) + 3) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1200 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(-5(3sin(3π((2x + 2)/(-1x - 3)) - 2) - 2)^2 - 4(3sin(3π((2x + 2)/(-1x - 3)) - 2) - 2) + 1) + 1| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 76 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3sin(3π((3(-1(-5x - 2) + 2) - 3)/(-2(-1(-5x - 2) + 2) - 3))) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2|(4(-1|((2x + 3)/(-1x + 3)) - 2| + 2) - 5) - 1| - 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) = -5(2(1sin(2π(2|x - 2| + 2) + 3) - 1) + 3) - 5 where -10 ≤ x ≤ 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) = 2cos(1π(1(-4(-1|x + 3| + 3)^2 - 1(-1|x + 3| + 3) + 2)^2 - 1(-4(-1|x + 3| + 3)^2 - 1(-1|x + 3| + 3) + 2) - 3) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1285 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2(2|((3(-1x^2 - 3x + 1) + 2)/(-3(-1x^2 - 3x + 1) + 4)) - 3| + 1)^2 - 3(2|((3(-1x^2 - 3x + 1) + 2)/(-3(-1x^2 - 3x + 1) + 4)) - 3| + 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation 1cos(1π(-5(-1(2x)^2 - 2(2x) + 3) - 3) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1161 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(-1sin(1π(-3|(-2x - 3) + 2| - 2) - 3) - 2)^2 - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 122 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2|(3|(1cos(3π(-2x + 1) + 3) + 1) - 1| - 1) - 3| - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 119 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-5(-3cos(2π(-3|x - 1| + 2) - 2) + 2) + 3) + 2 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) = (2((-2(-2cos(1π(1x - 3) + 1) + 1) + 2)/(3(-2cos(1π(1x - 3) + 1) + 1) - 1)) + 3)/(2((-2(-2cos(1π(1x - 3) + 1) + 1) + 2)/(3(-2cos(1π(1x - 3) + 1) + 1) - 1)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 20 | MATH |
[
{
"content": "How many solutions does the equation -5(1|(-3(3|x - 1| - 3))| - 1) + 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) = 3|(2sin(3π(-1|(3x - 3) - 2| + 3)) - 2) + 1| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 82 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2|((2(-3(2|x + 2|) + 2) + 1)/(-1(-3(2|x + 2|) + 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) = 2|(4(1(1x - 3) + 3)^2 - 5(1(1x - 3) + 3) - 1)| - 2 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) = -5(-1cos(2π((-2((2x + 2)/(-3x - 1)))/(1((2x + 2)/(-3x - 1)) + 1)) - 2))^2 + 1(-1cos(2π((-2((2x + 2)/(-3x - 1)))/(1((2x + 2)/(-3x - 1)) + 1)) - 2)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 182 | MATH |
[
{
"content": "How many solutions does the equation 3(-2(-3(1x + 2)^2 + 5(1x + 2) + 1) + 1)^2 - 4(-2(-3(1x + 2)^2 + 5(1x + 2) + 1) + 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(2(1(-2|x - 2| - 2) + 1) + 4)^2 - 1(2(1(-2|x - 2| - 2) + 1) + 4) - 4 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) = (-2(-3|(1cos(3π((-3x - 1)/(-1x + 3))))| + 1) - 3)/(1(-3|(1cos(3π((-3x - 1)/(-1x + 3))))| + 1)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 239 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2((-3(-3(3sin(3πx + 2) + 2)^2 + 5(3sin(3πx + 2) + 2) + 3) - 1)/(-3(-3(3sin(3πx + 2) + 2)^2 + 5(3sin(3πx + 2) + 2) + 3) - 2)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 47 | MATH |
[
{
"content": "How many solutions does the equation -1sin(3π(-5(-4((3x - 3)/(-2x + 1)) + 2)^2 + 5(-4((3x - 3)/(-2x + 1)) + 2) - 3) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 488 | MATH |
[
{
"content": "How many solutions does the equation -2(2(-4(3sin(3πx + 1) - 2)^2 + 4) + 2)^2 + 3(2(-4(3sin(3πx + 1) - 2)^2 + 4) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 65 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1|(-1|((-2(1sin(2πx + 3) + 2) - 2)/(2(1sin(2πx + 3) + 2) - 3)) + 2| + 1)| - 2 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) = -5(3((1(3x + 4) - 2)/(2(3x + 4) + 3))^2 + 2((1(3x + 4) - 2)/(2(3x + 4) + 3)) - 3)^2 + 4(3((1(3x + 4) - 2)/(2(3x + 4) + 3))^2 + 2((1(3x + 4) - 2)/(2(3x + 4) + 3)) - 3) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3(-2|(-1(1|x - 1| - 3) + 2)| + 2) + 1 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) = (-3(-1|(1|(3x) + 3| - 1) - 1| + 2) + 2)/(2(-1|(1|(3x) + 3| - 1) - 1| + 2) + 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) = 1sin(2π(-5((-1((2x - 2)/(1x)) + 3)/(2((2x - 2)/(1x)) + 2)) - 2) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 49 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 5(-3|(-3cos(3π(-3x^2 + 5x - 4) + 2)) + 1|) + 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 432 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (2(2sin(2π(2(2|x + 3|)^2 - 1(2|x + 3|)) - 1)) + 2)/(3(2sin(2π(2(2|x + 3|)^2 - 1(2|x + 3|)) - 1)) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1068 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1(-1sin(2π(-1((-2x + 3)/(1x + 1)) + 4) + 3)) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1e^(-1(-1(2|(-3x^2 - 5x - 2) + 3| - 2)^2 - 5(2|(-3x^2 - 5x - 2) + 3| - 2) + 4)) + 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) = (3((-1(-4(3sin(2πx + 3) + 2) + 3) - 2)/(3(-4(3sin(2πx + 3) + 2) + 3) - 2)) + 2)/(-3((-1(-4(3sin(2πx + 3) + 2) + 3) - 2)/(3(-4(3sin(2πx + 3) + 2) + 3) - 2)) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 40 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -5(5(-4(-3x^2 + 5x - 1) - 5)^2 + 2(-4(-3x^2 + 5x - 1) - 5) - 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) = 2e^(-1(-3|(-3|((1x - 1)/(-2x - 1)) + 3| + 2) + 2| + 2)) - 2 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(2((1(3cos(3πx) - 1) - 3)/(1(3cos(3πx) - 1)))^2 + 5((1(3cos(3πx) - 1) - 3)/(1(3cos(3πx) - 1))) + 5) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(1π((-2(4(-3|x + 2| + 2)^2 - 1(-3|x + 2| + 2) - 1) + 2)/(3(4(-3|x + 2| + 2)^2 - 1(-3|x + 2| + 2) - 1) + 3)) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 5(3(5((1x + 1)/(-1x - 3))^2 - 1((1x + 1)/(-1x - 3)) - 4)^2 + 1(5((1x + 1)/(-1x - 3))^2 - 1((1x + 1)/(-1x - 3)) - 4) - 1) + 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) = 5(-3((1(3sin(3πx + 1) + 3) - 3)/(1(3sin(3πx + 1) + 3))) - 2) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-2((1(-3sin(2π(-2|x - 2|) + 1) + 1) - 3)/(-2(-3sin(2π(-2|x - 2|) + 1) + 1) - 2)))/(2((1(-3sin(2π(-2|x - 2|) + 1) + 1) - 3)/(-2(-3sin(2π(-2|x - 2|) + 1) + 1) - 2)) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 80 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 4(-1|(-5(-5x^2 - 2x)^2 + 1(-5x^2 - 2x) + 2)| + 1) + 1 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) = -2cos(3π(-1((3(-4x - 2) + 3)/(-1(-4x - 2) + 3))^2 + 5((3(-4x - 2) + 3)/(-1(-4x - 2) + 3)) + 2) + 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 283 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(-3(2|(2sin(1πx + 1) + 2) - 1|)^2 - 4(2|(2sin(1πx + 1) + 2) - 1|) + 3)| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (2(3sin(2π((2(1x - 4) + 2)/(-2(1x - 4) + 3)) + 3) - 1) - 1)/(1(3sin(2π((2(1x - 4) + 2)/(-2(1x - 4) + 3)) + 3) - 1)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "How many solutions does the equation (-1(3|(-1(3sin(2πx + 2) + 2)^2 + 5(3sin(2πx + 2) + 2)) + 2| - 2) + 2)/(-3(3|(-1(3sin(2πx + 2) + 2)^2 + 5(3sin(2πx + 2) + 2)) + 2| - 2) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3((2(-1(-3sin(1πx - 1) - 3)) + 1)/(1(-1(-3sin(1πx - 1) - 3)) - 2)) - 3)/(3((2(-1(-3sin(1πx - 1) - 3)) + 1)/(1(-1(-3sin(1πx - 1) - 3)) - 2))) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 20 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (3((2(-2sin(1π(-1x + 3) - 2) - 2) + 1)/(-1(-2sin(1π(-1x + 3) - 2) - 2) - 1)) + 3)/(1((2(-2sin(1π(-1x + 3) - 2) - 2) + 1)/(-1(-2sin(1π(-1x + 3) - 2) - 2) - 1))) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 10 | MATH |
[
{
"content": "How many solutions does the equation 4(1cos(1π(-1|(1|x + 1| + 3) - 3| - 2)) - 2) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "How many zeros does the function f(x) = 4(-3cos(1π(-5(-2x^2 + 4x - 4)^2 - 4(-2x^2 + 4x - 4) + 1) - 1) + 3) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 841 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(2π(3(-3(3|x + 1| + 2)^2 - 5(3|x + 1| + 2) - 3)^2 + 3(-3(3|x + 1| + 2)^2 - 5(3|x + 1| + 2) - 3) + 1) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 414 | MATH |
[
{
"content": "How many solutions does the equation 1(-4(-2sin(2π((-3x)/(-3x + 2)) + 3) + 1)^2 - 2(-2sin(2π((-3x)/(-3x + 2)) + 3) + 1) + 3)^2 - 5(-4(-2sin(2π((-3x)/(-3x + 2)) + 3) + 1)^2 - 2(-2sin(2π((-3x)/(-3x + 2)) + 3) + 1) + 3) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\box... | 35 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-1(-4(-2|(3|x| - 3) + 2| + 3)^2 + 4(-2|(3|x| - 3) + 2| + 3) + 5) + 3)/(3(-4(-2|(3|x| - 3) + 2| + 3)^2 + 4(-2|(3|x| - 3) + 2| + 3) + 5) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 6 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (2(-3(1(2|x| - 2)^2 + 3(2|x| - 2) - 1)^2 - 3(1(2|x| - 2)^2 + 3(2|x| - 2) - 1) + 2) + 2)/(-3(-3(1(2|x| - 2)^2 + 3(2|x| - 2) - 1)^2 - 3(1(2|x| - 2)^2 + 3(2|x| - 2) - 1) + 2)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{You... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3sin(2π(-2|(3|((-2x + 2)/(-1x + 3)) + 3|) - 1| - 2)) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 215 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (1(5(-1(-5x + 1)^2 - 4(-5x + 1) + 5)^2 + 2) - 3)/(1(5(-1(-5x + 1)^2 - 4(-5x + 1) + 5)^2 + 2) + 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) = 3(-3sin(3π(1|((-2x + 3)/(-1x)) - 2| + 2) - 2)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 101 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(-4(-3(-3cos(1πx) - 1)^2 + 2(-3cos(1πx) - 1) + 1) - 2) + 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|(2cos(1π(-1|(3x^2 - 5x - 5) + 3|) - 1) - 3) + 1| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 586 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2(1e^(2((1(-1x^2 - 5x - 3))/(-1(-1x^2 - 5x - 3) + 2))) - 3)^2 - 3(1e^(2((1(-1x^2 - 5x - 3))/(-1(-1x^2 - 5x - 3) + 2))) - 3) - 4 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) = (-3(2(-1(3|x + 2| - 3)^2 - 4(3|x + 2| - 3) + 1)^2 + 3(-1(3|x + 2| - 3)^2 - 4(3|x + 2| - 3) + 1) - 3) - 1)/(2(2(-1(3|x + 2| - 3)^2 - 4(3|x + 2| - 3) + 1)^2 + 3(-1(3|x + 2| - 3)^2 - 4(3|x + 2| - 3) + 1) - 3) - 1) where -10 ≤ x ≤ 10.\n\nPresent t... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3sin(2π(5(-1|(-1x + 1) - 1| + 2) + 3)) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2((3(3|(3|x + 3| - 2) - 2| - 3))/(3(3|(3|x + 3| - 2) - 2| - 3) - 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) = 2sin(3π(-2(-2|(5x^2 - 5) + 2| + 3) - 1) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1129 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(-5(2cos(3π((3x - 2)/(-2x)) - 2) + 2) + 4) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 57 | MATH |
[
{
"content": "How many solutions does the equation -5((-2(3(-3cos(3πx - 2) + 2)^2 + 4(-3cos(3πx - 2) + 2) + 1) + 2)/(-2(3(-3cos(3πx - 2) + 2)^2 + 4(-3cos(3πx - 2) + 2) + 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 zeros does the function f(x) = -5((-2(2|(2|x - 2|) - 1|) - 3)/(3(2|(2|x - 2|) - 1|) + 1))^2 - 5((-2(2|(2|x - 2|) - 1|) - 3)/(3(2|(2|x - 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": "Determine the number of values x in [-10, 10] where f(x) = 2sin(1π(2(5(-3x^2 - 2x - 1) - 1) - 2) - 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 995 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2((3(1cos(2π((3x - 1)/(-1x + 2)) + 2)) - 1)/(2(1cos(2π((3x - 1)/(-1x + 2)) + 2)) + 3)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 106 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2(-2|(1(1|x + 3| + 1)^2 - 2(1|x + 3| + 1) - 3)| + 2) - 5 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|(-2|(3e^(2((2x - 3)/(3x - 1))) - 3) - 1| + 2) + 1| + 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) = 2cos(3π(-5(-1|(5x^2 - 5x + 2) + 2| + 1)^2 + 1(-1|(5x^2 - 5x + 2) + 2| + 1) + 5) - 1) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 644 | MATH |
[
{
"content": "How many solutions does the equation -2(-5(-3sin(2π((3x - 3)/(2x + 1)) - 2) - 3)^2 + 2(-3sin(2π((3x - 3)/(2x + 1)) - 2) - 3) + 5)^2 - 5(-5(-3sin(2π((3x - 3)/(2x + 1)) - 2) - 3)^2 + 2(-3sin(2π((3x - 3)/(2x + 1)) - 2) - 3) + 5) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex form... | 19 | MATH |
[
{
"content": "How many solutions does the equation 5(2(2|(2|x + 1| - 3)| + 1)^2 - 2(2|(2|x + 1| - 3)| + 1))^2 - 1(2(2|(2|x + 1| - 3)| + 1)^2 - 2(2|(2|x + 1| - 3)| + 1)) - 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) = (-3(2(-4((-3x + 1)/(-1x + 2))^2 + 3((-3x + 1)/(-1x + 2)) + 5)^2 + 1(-4((-3x + 1)/(-1x + 2))^2 + 3((-3x + 1)/(-1x + 2)) + 5) - 3) + 1)/(1(2(-4((-3x + 1)/(-1x + 2))^2 + 3((-3x + 1)/(-1x + 2)) + 5)^2 + 1(-4((-3x + 1)/(-1x + 2))^2 + 3((-3x + 1... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-1(2sin(2π((1((3x + 3)/(-2x + 1)) - 1)/(-3((3x + 3)/(-2x + 1)))) - 3) - 1) - 3)/(2(2sin(2π((1((3x + 3)/(-2x + 1)) - 1)/(-3((3x + 3)/(-2x + 1)))) - 3) - 1) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 21 | MATH |
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