@Carl Love 

As I said before, I extended the code which is in Maple centre from two variables to 4 variables. The original code works without adding x1 and x2 inside the function. With respect to your advice, I will leave all my interest in researching and will be included in classes teaching numerical and computer programming.

But extended code with error 99.9 is an excellent job to mine.

Amr

@mmcdara Thanks for your help. The colors take only one color.

Really it is very nice. Thanks a lot

Amr

@vv Thanks a lot it is very nice

Thanks a lot, it is very nice

@Kitonum Thanks a lot

I calculate this integration by Mathematica by using NIntegrate and with respect to singularities it was avoided and I get a discrete curve 

I need to calculate by Maple, where the function U(x,z) is defined  as follows

Now I want to integrate this function w.r.t x in the interval [0,10] to get another function as :

where the new function U1(y,z) is a function in two variables y and z.

Thanks a lot, but the function is defined in the first picture and.

with respect to Kitonum    the procedure is working for simple function but for the original function, it takes a lot of time. So I need a fast procedure

Is there a fast  numerical method

.Of course, there are a lot of singularities. But Mathematica can calculate this function with its singularities.

@tomleslie  Thanks

@Rouben Rostamian  

Dear Rouben Rostamian 

If I want to do this problem with contourplot3d is this possible

Amr 

@Rouben Rostamian  Thanks a lot

Dear Christian, could you give more explanation, because the procedure does not work

@Kitonum  Thanks a lot