Many thanks for your detailed response...

I'm working through your suggestions (their effect sounds like a miracle for me)

Many thanks for your detailed response...

I'm working through your suggestions (their effect sounds like a miracle for me)

@Robert Israel I do apolagize if I have bothered you, I didn't mean it.

yes, something like this will help. Function definition is also correct but it fails at zero points of r and z, because in the integrand there is (for example) r*cos(teta) , by subsituting r=0 this one will be eliminated from integration which sounds wrong.

I have now 3 other questions. I will be glad if you (or any other person) could help me... 

1. Is it possible for Maple to compute an integral false?

2. How can we reduce the computation time for an integral?(Still I have not examined your latest command line) Does Maple run slower than Mathlab for a similar program?

3. while running my program an error report appeared: "kernel connection has been lost" and it stopped running, needed to be restarted. How can I avoid this error?

Many Thanks...

@Robert Israel I do apolagize if I have bothered you, I didn't mean it.

yes, something like this will help. Function definition is also correct but it fails at zero points of r and z, because in the integrand there is (for example) r*cos(teta) , by subsituting r=0 this one will be eliminated from integration which sounds wrong.

I have now 3 other questions. I will be glad if you (or any other person) could help me... 

1. Is it possible for Maple to compute an integral false?

2. How can we reduce the computation time for an integral?(Still I have not examined your latest command line) Does Maple run slower than Mathlab for a similar program?

3. while running my program an error report appeared: "kernel connection has been lost" and it stopped running, needed to be restarted. How can I avoid this error?

Many Thanks...

 Dear Prof. Israel,

First it sounds right, but now..

Now I’ve examined the function and have found that with the procedure you suggested, Maple first put the numerical values of r and z into the complicated function f(r,z) and then compute the integral over the third parameter!!

What shall I do? There must be some numerical way of computing the integral of such complicated functions, but what??

 Dear Prof. Israel,

First it sounds right, but now..

Now I’ve examined the function and have found that with the procedure you suggested, Maple first put the numerical values of r and z into the complicated function f(r,z) and then compute the integral over the third parameter!!

What shall I do? There must be some numerical way of computing the integral of such complicated functions, but what??

Thanks a lot for your answer, it works..

I wanted to find an answer for the integral in the form of function (of r & z), and then substitute the numbers. but now with the procedure you suggested, Maple can find the answer immediately.

Thanks a lot for your answer, it works..

I wanted to find an answer for the integral in the form of function (of r & z), and then substitute the numbers. but now with the procedure you suggested, Maple can find the answer immediately.