instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Let v = -78 + -882. What is v rounded to the nearest one hundred?\n | -1000\n | ibivibiv/math_instruct | |
Is 65195826407 prime?\n | False\n | ibivibiv/math_instruct | |
Suppose 117*x + 143*x**4 - 120*x**3 + 3*x**5 + 69*x**2 - 183*x**2 - 46*x**4 + 17*x**4 = 0. What is x?\n | -39, -1, 0, 1\n | ibivibiv/math_instruct | |
Let t(c) be the second derivative of -c**3/6 - c. Suppose 13783 - 13765 = 9*q. Let k(a) = 9*a. Calculate q*k(j) + 21*t(j).\n | -3*j\n | ibivibiv/math_instruct | |
Simplify (u**(-13)/(u/(u/(u*u/(u*(((u**(7/8)/u)/u)/u)/u)))))/((((u/u**(-2/9))/u)/u)/u**(-3)) assuming u is positive.\n | u**(-1393/72)\n | ibivibiv/math_instruct | |
Suppose -41*a + 45*a = -26576. Let r be (-944)/a + (-2)/11. Is r not equal to 1?\n | True\n | ibivibiv/math_instruct | |
Convert 0.8943946t to grams.\n | 894394.6\n | ibivibiv/math_instruct | |
How many grams are there in 7/2 of a kilogram?\n | 3500\n | ibivibiv/math_instruct | |
Suppose -3*i = -15, 2*w - 2*i - 7280 = 20428. Is w a prime number?\n | True\n | ibivibiv/math_instruct | |
Expand ((-p + 3*p - 3*p)*(11 + 4 - 9) + 17*p - 38 + 38)*(-5*p**3 + p**3 + 3*p**3).\n | -11*p**4\n | ibivibiv/math_instruct | |
What is the second biggest value in -1/3, 2, 4, -0.27, -13/5?\n | 2\n | ibivibiv/math_instruct | |
Suppose -17*p - 113013 = -26*p. Is p a prime number?\n | False\n | ibivibiv/math_instruct | |
Let j be 26/6 - 1/3. Let s = -133 - -133. Solve u - j*u = s for u.\n | 0\n | ibivibiv/math_instruct | |
Suppose -2*n - 5*u + 1 + 3 = 0, -n + u = -2. Suppose 2*l = 3*l - n. Let h = 1 + l. Solve 0*t = h*t for t.\n | 0\n | ibivibiv/math_instruct | |
Expand 6*f + f**5 - 6*f - 2*f**5 + f**3 - f**3 + (3*f**4 - 4*f**4 - f**4)*(3*f - 4*f + 0*f) + 2*f**3 + f**5 - 2*f**3.\n | 2*f**5\n | ibivibiv/math_instruct | |
What is the result of the following expression?
45.046 % 14.733 | 0.8470 | ibivibiv/math_instruct | |
Rearrange -o + 28 - 3*o**2 - 28 + 0*o to the form k*o + i + l*o**2 and give k.\n | -1\n | ibivibiv/math_instruct | |
Let l = -5 + 1. Let p = -143230/183 + 2348/3. Let z = 545/366 - p. Which is the nearest to 0? (a) -2/11 (b) l (c) z\n | a\n | ibivibiv/math_instruct | |
Let f = 22 + -19. Calculate the remainder when 7 is divided by 5 - (f + (2 - 5)).\n | 2\n | ibivibiv/math_instruct | |
Let n = 4 - 0. Let p = -1.37 + -1.63. Let w = 2.4 - 2. Which is the nearest to 0.1? (a) p (b) n (c) w\n | c\n | ibivibiv/math_instruct | |
Let a(d) = -d**3 + 21*d**2 + 2*d - 45. Let v be a(21). What is the nearest to v in -2/9, 0.1, 6?\n | -2/9\n | ibivibiv/math_instruct | |
Round 0.00205676716 to 3 dps.\n | 0.002\n | ibivibiv/math_instruct | |
What is 660 minutes after 7:33 PM?\n | 6:33 AM\n | ibivibiv/math_instruct | |
Simplify p**14/p**15 assuming p is positive.\n | 1/p\n | ibivibiv/math_instruct | |
Let w(l) = 341*l + 3409. Let d be w(-10). Let m be ((3 + -2)*1)/1. Let a(h) = -5*h**3 + h**2 + 0*h + h**3 + 2*h + m. Calculate a(d).\n | 4\n | ibivibiv/math_instruct | |
What is the second biggest value in -0.2, 1, 1/3, 0.1, 1304?\n | 1\n | ibivibiv/math_instruct | |
What is the smallest common multiple of 12980 and 654310?\n | 14394820\n | ibivibiv/math_instruct | |
Let q(y) be the second derivative of y**6/10 + 3*y**5/10 - y**3 - 3*y**2/2 + 8*y. Factor q(f).\n | 3*(f - 1)*(f + 1)**3\n | ibivibiv/math_instruct | |
Evaluate 3 + (-79 + 90 - (20 + -3)).\n | -3\n | ibivibiv/math_instruct | |
Let n = -5 - -7. Suppose -4*v - 2 = -2*h, h = 3*v + 2*h - 6. Let u = n + v. Is 3 a factor of u?\n | True\n | ibivibiv/math_instruct | |
How many years are there in 0.0460163 millennia?\n | 46.0163\n | ibivibiv/math_instruct | |
Express 1531*d**3 - 511*d**3 - 56*d - 26*d - 508*d**3 + 30*d**2 - 511*d**3 in the form m + g*d**2 + z*d**3 + w*d and give z.\n | 1\n | ibivibiv/math_instruct | |
-11 (base 2) to base 8\n | -3\n | ibivibiv/math_instruct | |
Calculate 17632/(-266) + (-3)/21*(-6 + 8 + 3).\n | -67\n | ibivibiv/math_instruct | |
Let b = -6390 + 14321. Is b a multiple of 103?\n | True\n | ibivibiv/math_instruct | |
Let y = -2 - 3. Let m = y + 7. Let q be ((-9)/6)/((-30)/(-8)). Put m, 4, q in ascending order.\n | q, m, 4\n | ibivibiv/math_instruct | |
Solve -t - 3 = 2*g, -18*t = 5*g - 14*t + 12 for g.\n | 0\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 224 and 51313500.\n | 28\n | ibivibiv/math_instruct | |
What is the second derivative of -348288*k**2 - 892*k - 418?\n | -696576\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 2684 and 71581060.\n | 244\n | ibivibiv/math_instruct | |
Simplify (sqrt(75) + 2)**2 - (-1 + sqrt(18)/sqrt(6)).\n | 19*sqrt(3) + 80\n | ibivibiv/math_instruct | |
Solve -141 = 23*j - 26 for j.\n | -5\n | ibivibiv/math_instruct | |
Calculate -13 - 0.158137723.\n | -13.158137723\n | ibivibiv/math_instruct | |
Rearrange 2*l**4 - 3*l**3 - 4*l**4 + 712*l + 1 - 715*l to f*l**4 + w*l + y*l**3 + g*l**2 + q and give y.\n | -3\n | ibivibiv/math_instruct | |
Put together 5 and 0.2467.\n | 5.2467\n | ibivibiv/math_instruct | |
Suppose 20*p = 18*p + 728. Is 18 a factor of p?\n | False\n | ibivibiv/math_instruct | |
Let z(h) = -76*h + 200. Give z(3).\n | -28\n | ibivibiv/math_instruct | |
Which is the closest to -3? (a) -3 (b) 14.1 (c) 0.02 (d) 3 (e) -1/8\n | a\n | ibivibiv/math_instruct | |
Let U be the universal set and A be a subset of U such that A = {1, 3, 5, 7}. Find the complement of set A and show that the union of set A and its complement equals the universal set U. | To find the complement of set A, we need to determine the elements in the universal set U that are not in set A. However, we need more information about the universal set U to find the complement of set A.
For the sake of this problem, let's assume that the universal set U contains the integers from 1 to 10. In this ... | ibivibiv/math_instruct | |
Calculate prob of sequence sxgs when four letters picked without replacement from {e: 2, x: 1, s: 2, g: 2, t: 1}.\n | 1/420\n | ibivibiv/math_instruct | |
Simplify (s**(2/23)/s)/s**29*s**16*s*(s/(s**(-1/5)/s))/s assuming s is positive.\n | s**(-1347/115)\n | ibivibiv/math_instruct | |
Calculate the remainder when 16580 is divided by 5470.\n | 170\n | ibivibiv/math_instruct | |
Suppose 164437934*j**2/9 - 8*j/9 = 0. What is j?\n | 0, 4/82218967\n | ibivibiv/math_instruct | |
What is the next term in -184930, -369929, -554930, -739933, -924938, -1109945, -1294954?\n | -1479965\n | ibivibiv/math_instruct | |
b"What is the oth term of 15673, 16270, 16867, 17464?\n" | 597*o + 15076\n | ibivibiv/math_instruct | |
Is 303737 a multiple of 37?\n | False\n | ibivibiv/math_instruct | |
Let k = 225 + -192. Calculate the lowest common multiple of 42 and k.\n | 462\n | ibivibiv/math_instruct | |
What is 6.48308913 rounded to 3 dps?\n | 6.483\n | ibivibiv/math_instruct | |
Suppose 2*d - 10 = -c - c, 2*d + c - 10 = 0. Suppose -d*y - 3 = -4*y. Put 4, y, -4 in decreasing order.\n | 4, y, -4\n | ibivibiv/math_instruct | |
Product of -6 and -6.5905.\n | 39.543\n | ibivibiv/math_instruct | |
Let d(g) = 1613*g - 20 - 1614*g + 4. Give d(-7).\n | -9\n | ibivibiv/math_instruct | |
Let x = 371 - 386.1. Let b = x + 15.099999874. What is b rounded to 7 decimal places?\n | -0.0000001\n | ibivibiv/math_instruct | |
Solve 6 = 2*z + 4*t + 12, 8*t = -3*z - 7 for z.\n | -5\n | ibivibiv/math_instruct | |
Expand (-92*a**4 + 8*a**2 + 91*a**4 + 9*a**2)*(-5 - 3 + 1) - a**4 + 2*a**3 + a - a.\n | 6*a**4 + 2*a**3 - 119*a**2\n | ibivibiv/math_instruct | |
Which is the nearest to 1? (a) -2030 (b) -39 (c) 0.1 (d) 1 (e) 0\n | d\n | ibivibiv/math_instruct | |
What comes next: -247, -550, -865, -1198, -1555, -1942, -2365, -2830?\n | -3343\n | ibivibiv/math_instruct | |
List the prime factors of 2403380545.\n | 5, 480676109\n | ibivibiv/math_instruct | |
Solve w = x, -6*w + 2*w = -3*x - 1 for x.\n | 1\n | ibivibiv/math_instruct | |
Solve -20*r - 1202 + 437 = 25*r for r.\n | -17\n | ibivibiv/math_instruct | |
Factor 3*f**3 - 31052*f**2 - 321181*f - 103610.\n | (f - 10361)*(f + 10)*(3*f + 1)\n | ibivibiv/math_instruct | |
Which is the closest to -0.1? (a) 0.02 (b) -9 (c) -2 (d) -4\n | a\n | ibivibiv/math_instruct | |
Suppose 20 = 7*g - 3*g. Suppose -3*p - g*d + 22 = 0, -d = p + 4*d - 4. What are the prime factors of p?\n | 3\n | ibivibiv/math_instruct | |
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## Laplace equation in 2d problem, Dirichlet problem
1. The problem statement, all variables and given/known data
Consider a circle of radius a whose center is in (0,0). Let $(r, \phi)$ be the pola... | Beginning with the fundamentals, let us consider the Laplace equation, which is a second-order partial differential equation describing various physical phenomena such as electric potential, steady-state temperature distribution, and irrotational fluid flow. Its general form in Cartesian coordinates is:
∇²u = (∂²u/∂x... | ibivibiv/math_instruct | |
What is the second smallest value in 12, -25/18, 2?\n | 2\n | ibivibiv/math_instruct | |
Suppose -20 = -2308*n + 2318*n. Which is the nearest to -1/4? (a) -12/11 (b) n (c) -1\n | c\n | ibivibiv/math_instruct | |
Which is the nearest to 16.9? (a) 32/17 (b) -130 (c) 0.5\n | a\n | ibivibiv/math_instruct | |
Is 6/8 - (-24008050)/200 prime?\n | True\n | ibivibiv/math_instruct | |
What is 10680 to the power of 1/2, to the nearest integer?\n | 103\n | ibivibiv/math_instruct | |
Evaluate 12 + (24 - 27) - (14 - (2 + -4)).\n | -7\n | ibivibiv/math_instruct | |
Let u be (-58)/522 - 32/36. Which is the closest to 159? (a) 1/4 (b) -0.2 (c) u\n | a\n | ibivibiv/math_instruct | |
Suppose -5*c + 7*q - 2*q = 10, 2*c - 12 = -2*q. Find the third derivative of -2*u**2 + u**6 + 6*u**2 - 2*u**6 + c*u**2 wrt u.\n | -120*u**3\n | ibivibiv/math_instruct | |
What is the next term in 9008, 11679, 8006, -2011, -18372?\n | -41077\n | ibivibiv/math_instruct | |
What are the prime factors of 116622?\n | 2, 3, 11, 19, 31\n | ibivibiv/math_instruct | |
Let l(g) = -1 - 6*g**2 - 4*g**3 + 3 + 3*g**2 + 0*g**2. Let k(d) = d**3 + d**2 - 1. Suppose -t = -5*x + 24, 0*t + 9 = -t + 2*x. Calculate t*l(c) + 2*k(c).\n | -2*c**3 - c**2\n | ibivibiv/math_instruct | |
18/12*4/(-69)*44/132\n | -2/69\n | ibivibiv/math_instruct | |
Which is the fourth smallest value? (a) -0.7 (b) 0.3 (c) 5 (d) -14\n | c\n | ibivibiv/math_instruct | |
What is the tens digit of 9968908?\n | 0\n | ibivibiv/math_instruct | |
Which is greater: 0 or 22/25?\n | 22/25\n | ibivibiv/math_instruct | |
What are the prime factors of 1068302?\n | 2, 29, 113, 163\n | ibivibiv/math_instruct | |
Let r(u) = -10 - 13*u - 7*u - 4 + 23*u. Let c(x) = -1. Let m(t) = t**3 - 8*t**2 + 6*t + 6. Let g be m(7). Let q(s) = g*r(s) + 6*c(s). Differentiate q(a) wrt a.\n | -3\n | ibivibiv/math_instruct | |
Simplify (-3 + 1*sqrt(475) + 2*sqrt(475)*2 + sqrt(475) + -2 + sqrt(684)*-2 + -5)**2.\n | -360*sqrt(19) + 6256\n | ibivibiv/math_instruct | |
Express -10*g**2 + 8*g**2 - 17 + 24 - 3 - 10*g**3 in the form m*g**2 + f*g + v + h*g**3 and give m.\n | -2\n | ibivibiv/math_instruct | |
Let f be (-758)/14*(-77 + 93). Let c = f + 872. Solve -6/7*t**4 + 2/7*t**5 + c*t**2 + 128/7 + 192/7*t - 32/7*t**3 = 0 for t.\n | -2, -1, 4\n | ibivibiv/math_instruct | |
Rearrange (-1 + 3 - 1)*(-2*x + 4*x - 4*x + 8 - 8 - 8*x + (0 + 0 - 2)*(1 + 2*x - 1)) to r*x + f and give r.\n | -14\n | ibivibiv/math_instruct | |
Simplify (w*w**(-8))**(-4/27) assuming w is positive.\n | w**(28/27)\n | ibivibiv/math_instruct | |
Suppose 55 = -2*l + 7*l. Suppose 30 = 843*p - 833*p. What is the least common multiple of l and p?\n | 33\n | ibivibiv/math_instruct | |
What is the third derivative of -6*d + 2*d + 399*d**6 + 305210*d**2 + 1 - 1 - 305236*d**2 wrt d?\n | 47880*d**3\n | ibivibiv/math_instruct | |
Is 707 a multiple of 16?\n | False\n | ibivibiv/math_instruct | |
Suppose -2218 = 3*b - 2203, -5*b - 13 = -3*s. Let l = -3 + 4. What is the nearest to l in s, 4.2, 4?\n | 4\n | ibivibiv/math_instruct | |
Convert 5 (base 11) to base 16.\n | 5\n | ibivibiv/math_instruct |
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