@Kitonum 

Thanks

@Kitonum 

Thanks for your attention

Consider

g:=(x,k)->Int(exp(k*cos(z)), z = 0 .. x):

h:=(u,v,k1,k2)->int(exp(sin(g^-1(x,k1))*sin(g^-1(y,k2))), [x = 0..u, y = 0..v])

How can we plot and calculat h(u,v)?

@Kitonum 

Thanks for your answer

but if we considere

g:=unapply(int(exp(cos(z))), z = 0 .. x), x);  

h:=unapply(solve(y=g(x), x, explicit), y);   

we get this 

Error, (in solve) cannot solve expressions with int(exp(cos(z)), z = 0 .. x) for x