How to do numerical integral where the answer still have variables in it?

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The general answer is no. In your case, you can easily isolate h and d since $exp(x+y)=exp(x)+exp(y)$. Note also that the integral can be computed symbolically:

sage: var('d h')
(d, h)
sage: integral(exp(-(h-1)^2-(d-2)^2), d,0,Infinity)
1/2*sqrt(pi)*erf(2)*e^(-h^2 + 2*h - 1) + 1/2*sqrt(pi)*e^(-h^2 + 2*h - 1)