instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Let p(o) = -2*o**3 + o**2 + 19*o - 14. Calculate p(5).\n | -144\n | ibivibiv/math_instruct | |
Let j = -1266 - -1264. What is the second smallest value in 18/11, 4/7, j?\n | 4/7\n | ibivibiv/math_instruct | |
What is the next term in -25328, -25332, -25336, -25340, -25344, -25348?\n | -25352\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {r: 1, o: 2, f: 2, c: 1, a: 1, u: 1}. What is prob of picking 1 c and 1 r?\n | 1/28\n | ibivibiv/math_instruct | |
Suppose -5*b + 34 = -t - 539, 0 = 3*b - t - 345. Calculate the greatest common divisor of 1216 and b.\n | 38\n | ibivibiv/math_instruct | |
In base 2, what is -10 - 110111001110?\n | -110111010000\n | ibivibiv/math_instruct | |
Calculate prob of sequence hxh when three letters picked without replacement from hxxxxxxxxxxxxxxhxxx.\n | 1/171\n | ibivibiv/math_instruct | |
How many minutes are there between 3:48 AM and 5:32 AM?\n | 104\n | ibivibiv/math_instruct | |
How many millilitres are there in five quarters of a litre?\n | 1250\n | ibivibiv/math_instruct | |
Rearrange 318 - 96 + 5*q - 3*q + 722 - 69 to the form g + m*q and give m.\n | 2\n | ibivibiv/math_instruct | |
Calculate (459/(-153))/((-2)/((-16)/6)).\n | -4\n | ibivibiv/math_instruct | |
Let c be (-58)/(-14) - (-5)/(-35). Solve -q + 6 = 5*j, -4*j + 3*j + c*q = -18 for j.\n | 2\n | ibivibiv/math_instruct | |
Calculate 2147*-2061.\n | -4424967\n | ibivibiv/math_instruct | |
Let x(n) = 87*n**2 - 1603*n - 9592. Determine x(-6).\n | 3158\n | ibivibiv/math_instruct | |
Which is the closest to -293? (a) -1/67 (b) 31.5 (c) 3/2\n | a\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {i: 1, p: 1, u: 1, f: 2, k: 1, n: 1}. What is prob of picking 1 k and 1 u?\n | 1/21\n | ibivibiv/math_instruct | |
Sort -1, 0, -16, 3, 344, 5 in decreasing order.\n | 344, 5, 3, 0, -1, -16\n | ibivibiv/math_instruct | |
Let z = 158/47 - 8623/1880. What is the common denominator of z and (4/((-1024)/(-1320)))/((-6)/(-8))?\n | 40\n | ibivibiv/math_instruct | |
Let a(f) = -f + 4*f - 2*f**2 + 3*f**2. Let o be a(-3). Suppose 0 = 5*s - 6 - 4. What is the second smallest value in o, s, 2/3?\n | 2/3\n | ibivibiv/math_instruct | |
Which is smaller: 0 or -1940/6127?\n | -1940/6127\n | ibivibiv/math_instruct | |
Is 695452993 a prime number?\n | False\n | ibivibiv/math_instruct | |
What is next in 47357, 47842, 48319, 48788, 49249?\n | 49702\n | ibivibiv/math_instruct | |
Convert 338 (base 16) to base 7.\n | 2255\n | ibivibiv/math_instruct | |
Let a = -203 + 207. Calculate the highest common divisor of 28 and a.\n | 4\n | ibivibiv/math_instruct | |
Let l be 8868/15 + -4 + 2. Let h = 587 - l. Which is bigger: h or -3?\n | h\n | ibivibiv/math_instruct | |
Calculate the remainder when 302 is divided by 76.\n | 74\n | ibivibiv/math_instruct | |
Evaluate -2*33/90 - (-8)/24.\n | -2/5\n | ibivibiv/math_instruct | |
Let c(p) = -512500*p**2. Let b be c(2). What is b rounded to the nearest 1000000?\n | -2000000\n | ibivibiv/math_instruct | |
Let f(v) = 2*v. Let m(g) = -4*g**2 + 2*g - 539. What is m(f(j))?\n | -16*j**2 + 4*j - 539\n | ibivibiv/math_instruct | |
Solve -4*f - 3 = 5*i, 0 = 2*f + 21 - 17 for i.\n | 1\n | ibivibiv/math_instruct | |
List the prime factors of 520076921.\n | 7, 13, 37, 83, 1861\n | ibivibiv/math_instruct | |
Sort 3, 0.3, -4 in descending order.\n | 3, 0.3, -4\n | ibivibiv/math_instruct | |
Calculate -6108 + 6131 + (24 - -1).\n | 48\n | ibivibiv/math_instruct | |
Suppose v - 6 = -2*b, -2*b + 3*v = -5*b + 12. Suppose b*i - 16 = -4*h, 7 = 5*h - i - 6. Suppose 0 = -l + h*l - 11600000. Round l to the nearest 1000000.\n | 6000000\n | ibivibiv/math_instruct | |
Suppose -p - 13 = 3*u, -2*p + 20 = 3*p - 2*u. Suppose 7 = -p*a + 3. Suppose -38*h + 35*h + 9 = 0. Sort h, a, 0.\n | a, 0, h\n | ibivibiv/math_instruct | |
Let u(i) = -3*i + 4. Suppose 0*z - 2*z = -8. Suppose -z*h = -h. Let t(w) = -w + h*w + 2*w - 1. Calculate -2*t(r) - u(r).\n | r - 2\n | ibivibiv/math_instruct | |
Let i(j) = -j**3 - 4527*j**2 - 94632*j - 27. What is i(-21)?\n | 99\n | ibivibiv/math_instruct | |
Collect the terms in -o**2 + 8*o**2 + 6*o**2 + 0*o**2 + 0*o**2 + 0*o**2.\n | 13*o**2\n | ibivibiv/math_instruct | |
Is 34 a factor of 914020?\n | False\n | ibivibiv/math_instruct | |
Let g = -50 - -69. Let v = -4 + 14. Calculate the remainder when g is divided by v.\n | 9\n | ibivibiv/math_instruct | |
Suppose 5*b = 3 + 12. What is the tens digit of (-4)/54*b + (-1750)/(-18)?\n | 9\n | ibivibiv/math_instruct | |
Differentiate 5*f**3 + 6*f - 466 wrt f.\n | 15*f**2 + 6\n | ibivibiv/math_instruct | |
Let s(v) = 26*v - 156. Let n(t) = 1. What is 156*n(k) + s(k)?\n | 26*k\n | ibivibiv/math_instruct | |
Simplify (1*sqrt(45)*-6)/(-4*sqrt(9)*2).\n | 3*sqrt(5)/4\n | ibivibiv/math_instruct | |
Let z = 1386 + 2403. What is the units digit of z?\n | 9\n | ibivibiv/math_instruct | |
Let m(u) = 153208*u - 871651. Let q(j) = -9821*j + 55875. Let k(d) = -12*m(d) - 187*q(d). What is the first derivative of k(z) wrt z?\n | -1969\n | ibivibiv/math_instruct | |
Rearrange -8*v**4 + v**3 - 15*v**4 - 4 - 8*v**4 + 7 to the form x*v**4 + c*v**2 + t*v**3 + f + b*v and give t.\n | 1\n | ibivibiv/math_instruct | |
Simplify (v**(-2/7)*v)/v*v**4*v**6*v*v*v**7*(v**(1/3)*v**1)**(6/7) assuming v is positive.\n | v**(139/7)\n | ibivibiv/math_instruct | |
Let z = 242266 + -242265.942. Let m(y) = y. Let v be m(1). What is the closest to v in -2/7, -5/6, z?\n | z\n | ibivibiv/math_instruct | |
Find the common denominator of -117/28 and -23/16.\n | 112\n | ibivibiv/math_instruct | |
What is the ten thousands digit of 11049107?\n | 4\n | ibivibiv/math_instruct | |
Put 0.033, -3, -7.105 in ascending order.\n | -7.105, -3, 0.033\n | ibivibiv/math_instruct | |
Calculate the remainder when 1123 is divided by 229.\n | 207\n | ibivibiv/math_instruct | |
Is 61315 a prime number?\n | False\n | ibivibiv/math_instruct | |
What is -0.0587 rounded to three decimal places?\n | -0.059\n | ibivibiv/math_instruct | |
What comes next: 15, 43, 87, 147, 223, 315?\n | 423\n | ibivibiv/math_instruct | |
Is 323578667 composite?\n | True\n | ibivibiv/math_instruct | |
Suppose 6*b = -23*b + 2726. Let r = b + -73. What is the lowest common multiple of r and 27?\n | 189\n | ibivibiv/math_instruct | |
Is 22 a factor of 2349?\n | False\n | ibivibiv/math_instruct | |
Collect the terms in 6 + 34*k + 19 - 1 - 5.\n | 34*k + 19\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Adding a limit in NDSolve to avoid division by zero
I'm trying to solve a set of differential equations in which one of the functions that describe the time derivative gets values which make it divide by zero
x'[t] = (Exp... | When solving differential equations using numerical methods, encountering mathematical operations that result in undefined expressions, such as dividing by zero, can be a common issue. This problem occurs because numerical solvers typically cannot handle symbolic manipulations required to evaluate these indeterminate ... | ibivibiv/math_instruct | |
Let n(r) = -r + 1. Let l(w) = -4*w - 1. Let o(t) = l(t) - 2*n(t). Determine o(-6).\n | 9\n | ibivibiv/math_instruct | |
Sort -2/3, -1298, 17, 0, 1/3, 0.1.\n | -1298, -2/3, 0, 0.1, 1/3, 17\n | ibivibiv/math_instruct | |
Let x = 3.211 + 140.089. Let u = x - 143. Let k = 0.3 - -0.2. Put -2, k, u, -3 in ascending order.\n | -3, -2, u, k\n | ibivibiv/math_instruct | |
Is 12464053891 a composite number?\n | False\n | ibivibiv/math_instruct | |
Let x(c) = 5*c. Let w(d) be the second derivative of d**3/3 + 6*d. Calculate w(x(g)).\n | 10*g\n | ibivibiv/math_instruct | |
Three letters picked without replacement from wnnannoaoaanaawao. What is prob of picking 1 n and 2 a?\n | 21/136\n | ibivibiv/math_instruct | |
Find the common denominator of 103/22 and -89/50.\n | 550\n | ibivibiv/math_instruct | |
In base 9, what is -505 + 1?\n | -504\n | ibivibiv/math_instruct | |
Is 272778 a multiple of 389?\n | False\n | ibivibiv/math_instruct | |
What is the hundred thousands digit of 405690?\n | 4\n | ibivibiv/math_instruct | |
Find the third derivative of 36*n**5 - 3*n**4*v - 2*n**3*v + 2*n**2*v - 34*n*v - n wrt n.\n | 2160*n**2 - 72*n*v - 12*v\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 3 and 47.\n | 141\n | ibivibiv/math_instruct | |
Simplify ((sqrt(480)/(-2*sqrt(10)) + (2*sqrt(528))/sqrt(11))/((sqrt(384)/sqrt(192))/sqrt(8)))**2*-2 + -5.\n | -869\n | ibivibiv/math_instruct | |
Suppose 0*k - 5*j + 15 = 5*k, -4*j = -k + 18. Calculate the lowest common multiple of 30 and k.\n | 30\n | ibivibiv/math_instruct | |
Expand ((-4 + 0 + 2)*(-2*g - 3*g + 3*g) - 3*g + 5*g - g - 3*g + 4*g - 5*g)*(0 - 3 + 8)*(-3 - 5 + 5 + (-3 + 3 - 2)*(1 - 6 + 3) - 1 - 3 - 2).\n | -25*g\n | ibivibiv/math_instruct | |
Let q = -6 - -9. Let x = 5.9 + -6. Let a = -4 + 6. Sort x, a, q in ascending order.\n | x, a, q\n | ibivibiv/math_instruct | |
Find the common denominator of -73/128310 and 29/437570.\n | 17065230\n | ibivibiv/math_instruct | |
Collect the terms in -263 - 312841616*o**2 + 312841617*o**2 + 263.\n | o**2\n | ibivibiv/math_instruct | |
Calculate the remainder when 2196 is divided by 55.\n | 51\n | ibivibiv/math_instruct | |
What is -8*(-2)/((-272)/4)?\n | -4/17\n | ibivibiv/math_instruct | |
Let l(o) = o**3 - 45*o**2 - 6*o - 85. Is l(46) a multiple of 39?\n | True\n | ibivibiv/math_instruct | |
Find the first derivative of -7057*p**2 + 41*p + 1142479.\n | -14114*p + 41\n | ibivibiv/math_instruct | |
What is the sixth root of 272643406 to the nearest integer?\n | 25\n | ibivibiv/math_instruct | |
-29*0.16\n | -4.64\n | ibivibiv/math_instruct | |
What is 13704 to the power of 1/3, to the nearest integer?\n | 24\n | ibivibiv/math_instruct | |
What is -3214 (base 7) in base 2?\n | -10001110010\n | ibivibiv/math_instruct | |
Solve 10*j + 18 = 68 for j.\n | 5\n | ibivibiv/math_instruct | |
Let q = -123 + 81. Let z = 874.892 - 878. Let i = z - -0.108. Which is the third smallest value? (a) q (b) 5 (c) i\n | b\n | ibivibiv/math_instruct | |
Let a = 147/340 - 11/20. What is the nearest to 2/3 in -7, 0.4, a?\n | 0.4\n | ibivibiv/math_instruct | |
What is the greatest common factor of 90 and 690?\n | 30\n | ibivibiv/math_instruct | |
What is 0.5689 rounded to two dps?\n | 0.57\n | ibivibiv/math_instruct | |
Collect the terms in 316793700*i**2 - 316793697*i**2 - 4*i + 4*i.\n | 3*i**2\n | ibivibiv/math_instruct | |
Calculate the remainder when 629 is divided by 35.\n | 34\n | ibivibiv/math_instruct | |
Is 3453 a factor of 684077283?\n | True\n | ibivibiv/math_instruct | |
Suppose -78 = -18*m + 5*m. Solve -4 = -8*h + m*h for h.\n | 2\n | ibivibiv/math_instruct | |
Express (-41*q - 28*q + 22*q)*(21*q**3 - 24*q**3 + 0 - 8) in the form h*q + u*q**4 + c*q**3 + s + z*q**2 and give h.\n | 376\n | ibivibiv/math_instruct | |
What is 42580 to the power of 1/3, to the nearest integer?\n | 35\n | ibivibiv/math_instruct | |
Let r(u) = -u - 3. Let f be r(0). Let l be 1/(f/6) + 4. Determine z, given that z - 2*z - 3*z**l - z = 0.\n | -2/3, 0\n | ibivibiv/math_instruct | |
Express (-2*y + 0*y + y)*(247 - 3 + 840) as k + m*y and give m.\n | -1084\n | ibivibiv/math_instruct |
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