Question: fastest way of computing an integral numerically?

I'd like to numerically compute integrals of the forms:

int(exp(-t)/((-3+2*exp(-(1/10)*t))*(-3+2*exp(-(9/10)*t))), t = 0 .. infinity); evalf(%)

where there are much more terms in the denominator, e.g.,

Int(e^(-t)/(product(-3+2*exp(-.1*(1-.1)^i*t), i = 0 .. A)), t = 0 .. infinity); evalf(%)

for some positive integer A. Even when I have three terms it takes so long... So how do I compute such integrals numerically with maple; what's the efficient way? My understanding is that no explicit symbolical result can be ontained, e.g., for A=infinity, but I would be happy to be wrong!  

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