OK,I find maybe I should sovle this problem by using DirectSearch optimization package. Three new derivative-free optimization methods (Powell’s, Brent’s, and successive quadratic approximation) are added in that package.Does someone know how to use Powell’s method to solve my problem?

@Adam Ledger 

You are right!It's worth working on the code until it returns in a reasonable time frame.Thank's for your advice..And your experience is useful for me as well as for others.

My code is stilling running, I don't know if it will work out.I will make it run until tomorrow.

Maybe I should learn something about optimization algorithm in the furture,for solving the problem.And on the other hand,finding a way that can solve my problem faster.I have heard that some people solve  the problem like mine using Powell algorithm.But for the time being,I  need the help of  the nonlinearfit command in Maple.

@Adam Ledger 

Sorry to reply late!

It's interesting to imagine Maple as a person who is good at computation.

I haved  executed your code.And I found It really cost  a considerably long time to return an output.After it haved run for serveral hours,I stopped it and I wanted to see if I give the value of all parameters and plot the figure,what would happen.I found it also cost  a long time and didn't return an output.

I don't know why,because a few days ago,I have tried to give the value of all parameters first and  then plot the figure of the tripe integral function.I can get a figure successfully.The code can be saw in the attached,the first group.

And then I began to use Nonlinearfit command.But it has run for five hours and still be in the state of evaluating.I don't know if it can return me the values of that two parameters.I just let it play and continue to do other works.I will return to see if it  returns an output finally and tell you in time.

P.S. I think maybe it's important to give that two parameters initialvalues,as my code showed.20180526002.mw

@Adam Ledger OK,I can't get the correct answer.It seems the last error is removed.But then there are some new errors.

@Carl Love Thanks for your help!

I have tried to  turning the model into an arrow procedure and run it again.It seems the error is removed,but I can't  get an answer.As showed below,there are some other new errors.

This is my new code!

datax := [-8, -4.5, -.5, 4.5, 8, 11.5, 14.5];

datay := [0.287e-2, 0.266e-2, 0.259e-2, 0.199e-2, 0.164e-2, 0.113e-2, 0.78e-3];

p1 := plot(datax, datay, style = point, symbol = solidcircle, color = blue, symbolsize = 12);

f := proc (x) options operator, arrow; int(tan(beta)^2*exp(-Pi*tan(beta)^2*((x-varepsilon)^2+varsigma^2)/eta^2)/eta^2, [eta = 22.83-sqrt((5.83+`ΔA`)^2-varepsilon^2) .. 22.83+sqrt((5.83+`ΔA`)^2-varepsilon^2), varepsilon = -5.83-`ΔA` .. 5.83+`ΔA`, varsigma = -1 .. 1])-(int(tan(beta)^2*exp(-Pi*tan(beta)^2*((x-varepsilon)^2+varsigma^2)/eta^2)/eta^2, [eta = 22.83-sqrt(5.83^2-varepsilon^2) .. 22.83+sqrt(5.83^2-varepsilon^2), varepsilon = -5.83 .. 5.83, varsigma = -1 .. 1])) end proc;

z := Statistics[NonlinearFit](f, datax, datay, x); p2 := plot(z, x = datax[1] .. datax[-1], color = red);

plots[display](p1, p2);

Warning, calling NLPSolve as a constant objective function was found
Error, (in Statistics:-NonlinearFit) problem must have at least one variable
Error, (in plot) expected a range but received x = -8 .. 14.5
Error, (in plots:-display) expecting plot structure but received: p2

There must be some other mistakes in my code!How can I obtain correct parameter values?

@Adam Ledger 

Thanks for your help.

Actually,I started to use Maple several days ago and it is my first time to use this package.The code is showed in my question.If you run it and make any progress,please tell me.

 I am trying to solve this problem with your advice.If I  make any progress，I will talk to you right away.Thanks again!