@Carl Love @Kitonum Thank you for the answers. unanswered question gains 0 point.

@Carl Love actually i need opposite function of the Heaviside function, the case where if it is negetive it is 1 and when it is positive it is zero. Does maple have any function for this?( i've got my answer from above responses, only ask this for more knowledge).
 

@vv then what should i do for tau=0? how can simplify accounting for tau=0? is it possible?

@dharr thank you for your attention and your time.But if you look more carefully the denominator is not zero with sigma or tau equals zero.

@acer actually i have do this in lists. i asked if it is possible with sets or not?

 

Download setoder2.mw

@acer @Carl Love 
here is the problem

Download simplify_problem.mw

@acer if i store SS1 and SS2 in matrix, using simplify assuming real does NOT operates. is it a bug ?

@acer yes. Thank you 

@Kitonum yes you are right, maybe it is a bug in maple. I have another question, can this integral be solved symbolically as a function of T ?

@acer i know it can't , but what is wrong with maple? i put numeric option in the middle of the integration and it does give some answer( don't know wrong or true). my first question is why maple is behaving like this. and my second question is how can i get a true output of function T ?
 

@acer thank u, i unassinged the u[10] and the problem solved. thank u

@vv thnx for quick answer. is there a way to know number of repetitition of members in each set? for example [1,1,5]  1 twice and 5 once.
 

@vv thank you for your respone, how you evaluate thin integral like this? could plz explain the surface of integration

@Kitonum tnx for impressive answer,i have one more question, can the volume be computed?

@Kitonum yes you are right it is d3