@Carl Love yes I got the point. Thanks a lot.

@Carl Love in kitonum's last reply two x s used don't have any connection right? . As you said it is also just x spelled coincidentally. This is what I followed till date. Actually I am not able to understand the example of arrow function example provided by kitonum because as you said those two x s and t s are coincidentally spelled. If I am wrong please correct. Thank you.

@Carl Love ok 

restart;
x:=10:   #### global variable

ff:=proc(x:=5)

     return x^2:
    end proc:

ff();

ff(x);

output: 25   

            100

Thanks a lot to both of you in solving the doubts with clear cut examples. 

@Kitonum 

x:=10:t:=20:
f:=proc(x)
    return x^2:
    end proc:

here first x is a variable and the second x is a place holder, right?

@Kitonum 

Thanks a lot. Can you please tell the commands which have this exception or any manual for reading this. Since the source code is not available it is hard to understand this sort of thing. Thank you.

@Christopher2222 I guess this is the best one. TSprintf cannot work inside a loop.

@Carl Love

Thanks a lot. 

@Joe Riel  Yes. Thanks a lot.

@ecterrab The GUI is getting stuck each and every time and most of the time I am forced to kill the job from the terminal. 

@vv 

restart;

with(student);

Q := proc (a, b, c, d, x, y)

local t;

x^2-x+y^2-5*y-evalf(middlesum(5*exp(sin(t+x)), t = 0 .. b, 50)) :

end proc;

Optimization:-NLPSolve(Q(1, (1/2)*Pi, 5, 2, x, y), x = 0 .. 5, y = 0 .. 4)

answer----  [-25.8264566652271874, [x = .750454656153088, y = 2.50000000432744]]

@tomleslie Ok but the article which I referred above deals with such analysis. But as you said I think it cannot locate all.

@Kitonum YES. I have found a method called MinFinder proposed by Ioannis G. Tsoulos which does the same. May be direct search package may be using such method.

@tomleslie Ok thank a lot. 

@Carl Love Nice. I think it will be really great if the maple community can post some algorithms from various branches.

@Kitonum Ok thanks a lot.