Question: Evaluate then assign as function

Hello all, I know several people around my university that have had this problem so I finally thought I should ask: Lets say I have some complicated integral, the integrand is a function of several variables. If I: 1)simply evaluate it and I get some function of the remaining variables. 2)try to assign it such as A:=(x,y,z)-> integral, I get A(x,y,z)=integral what I want is to first evaluate to a function and then assign that function as some name as a function of the remaining variables. I know this must be possible, but I can't seem to get it. Thanks for the help. (I can provide an example if someone needs it)
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