@Markiyan Hirnyk In order to be constructive in your language, I suggest you to take a look at the link that "acer" has mentioned above and is repeated below:

http://www.phyast.pitt.edu/~zov1/gnuplot/html/contour.html

@acer I will be waiting to see the result of your work. Finally, someone is caring about this defect in Maple plotting! :)

Many Thanks and Good Luck! :)

@Markiyan Hirnyk I think it doesn't really matters that the contours are plotted using a numerical database or using an analytic expression. What I am looking for is that I want to display the value related to each curve.

It is really disappointing that maple doesn't have any automatic features for this! :)

@Markiyan Hirnyk The solution you suggested is not doable for complicated cases like the pic above since you should determine the "locus" of texts using "textplot" and it is not an easy job to do!

@acer Consider the constants C[1,0], B[1,0], C[1,i__1], B[1,i__1] in the equation. I also want that the integration be raplaced by the most inner coefficients of the aforementioned constants (which are functions of z) without altering anything else. For better understanding see the file below.

The reason for this is that I want to replace the Inert integrations using my own integration database in the next step. And again the reason for such a replacement is that maple do not integrate in the forms I want so I do the integration by hand and replace it using the "subs" command. :)

Equation-Integrated.mw

@Carl Love This method won't work for some complicated case because you must specify the "locus" of the text on the plot and it is a difficult task to do. take a look at the following picture.

@Kitonum It's realy disappointing that the "contourplot" doesn't have any options for this! :/
As always, maple has lots of problems in plotting! :)

@Carl Love Can you handle this with on the file "Example.mw"? :)

@Carl Love Can you explain what each command is doing? :)
Specially "try" and "catch" commands.

@Carl Love I guess that I should use Maple 18 too! :)

@Carl Love My maple is 17. Also I use win7 on a 32bit platfrom.
Can you tell me maple version, the computation time that maple gives and also the hardware that you are using?

Many thanks.
   

@Thomas Richard Thank for your help. :)

@Thomas Richard Can you tell me how much time does it take for differen values of N with prc=20? (N=10,N=50,N=100)
Try this code for computation of the time.

Example_2-R.mw

@Thomas Richard 

1- About the "digits" you saved me from a big mistake! :D
    I have forgotten that "Digits" should be used!

2- About the definition of "f(r)", It is not the main problem but you are right! :)

3- About the FR procedure, it may need some improvments, but it is not  the main problem. I don't know what are autocompile and hfloat! and I haven't used them.

4-About maple 18, I should try it! :)

5- Finally, the main problem: On my system when it reaches to the evalf at the beginnig of the Numerical Result section, it stops for a long time (more than 1000 seconds for N=100 !), so it seems that it has problems in numerically evaluating the integrals which are in A[i] (coefficients of SS).

6- Question: Does it stop for a noticeable time at the begining of Numerical Result section on your system?

@Carl Love That's strange. Do you have any idea that why it is not working fast for me? (It does finish but it take lots of time!)

The "N" parameter is in the "Input" section. You can see the pic below.
Can you provide me with your maple version, the computation time that maple gives and also the hardware that you are using?

My hardware: Intel Core 2 Due T9300 @ 2.5Ghz, 4GB RAM (3.5GB usable)