I just noticed something funny. If I use the left side tool of Maple to define a matrix with zero entries and then change some entries and take determinant, then Maple treats zeros as symbold!!!! If I have to define my matrix completely myself, then what is the use of this tool?

I have a multiple integration. I know my integrals exist. When I write procedure for Rimannian sum, Maple gives correct answers for every choice of parameters of my integral. But when I ask Maple to compute it with int(...,numeric) sometimes it shows a correct answer and sometimes it shows a wrong answer. I'm curios to know what is going wrong in Maple, is there any command to see the details and steps of the computation to see where Maple is going wrong? I also increased the number of digits after decimal from 10 to 12 and 14. But Maple just repeats the wrong answers with just two or four digits. So the problem is not related to the approximation arising from number of decimals.

I have a positive function and I'm taking an integral from it. I don't get why Maple computes the integral over a bigger region but not over a subset of it! Here is the integral. Does anyone know what is going wrong?

int(15.91549431*abs(6.100147120*10^6/k[6]-2.027358424*10^6*(1.241833982*k[6]/T[1]+2.)/k[6]+2.002942410*10^6/T[1])*exp(-50.00000000*(1.241833982*k[6]/T[1]-1.5)^2)/(k[6]^2*T[1]^2), T[1] = -.5 .. 0, k[6] = -.5 .. 0, numeric)

int(15.91549431*abs(6.100147120*10^6/k[6]-2.027358424*10^6*(1.241833982*k[6]/T[1]+2.)/k[6]+2.002942410*10^6/T[1])*exp(-50.00000000*(1.241833982*k[6]/T[1]-1.5)^2)/(k[6]^2*T[1]^2), T[1] = -.9 .. 0, k[6] = -.9 .. 0, numeric)

In the package Student[Calculus1], the NewTon-Cotes closed formulas are implemented. But I was thinking if there is any other package of Maple having the open Newton-Cotes Fromulas. I searched and I just saw in Student[NumericalAnalysis] for Quadratures.

Maple gives the integral's face instead of giving a number as the numerical integration, no matter what command for the numerical integration I use. Does any one know what the problem is?

T2start := -5.036645000*10^9*(x[5]^2+.2725890432*x[5]+.3732640349)*x[5]/(5.036645000*10^9*x[5]^2+1.27004241*10^8*x[5]+5.3714241*10^7); 
T2end := -5.036645000*10^9*(x[5]^2+.2871403962*x[5]+.3945934083)*x[5]/(5.036645000*10^9*x[5]^2+1.27004241*10^8*x[5]+5.3714241*10^7);
J := (25183225000000*x[5]^4+(-100732900000000*T[2]+73827142410000)*x[5]^3+(-112645777230000*T[2]+662242877289)*x[5]^2-2398770574578*T[2]*x[5]-393671672289*T[2])/(10000000*x[5]^2+14658000*x[5]);
int(abs(J), [T[2] = T2start .. T2end, x[5] = 0 .. infinity], numeric);

I also used the following.

evalf(Int(abs(J), [T[2] = T2start .. T2end, x[5] = 0 .. infinity]));

The result was same.

Or when I use

evalf(Int(abs(J), [T[2] = T2start .. T2end, x[5] = 0 .. infinity], method = _MonteCarlo));

It gives an error saying:

Error, (in evalf/int) invalid arguments