plot(sin(Pi*x)*exp(A*x),x=a..b) works for A=100 and all values of a and b I tried so Maple does plot it; I guess your question is really why we can not visualize this function well:
for large A, if you pick a narrow domain (a close to b), you can visualize well but you are essentially plotting the exponential function only as sin(Pi*x) does not vary that much for a close to b;
but if you pick a large domain, the highest (or lowest) peak of the function will be way higher than the other peaks (so you will not be able to see them because of the scale, all the other peaks are way closer to zero the to the top peak.
for some functions you can solve this type of problem by using a log scale, see logplot or loglogplot commands with the plots package but in your case I do not think that it would help without additional modifications...
if I had to present this function in a paper, I would present two plots, say one with a from 0 to 3, showing a peak at 2x10^128 and another plot with range from 0 to 1 with a peak at 3x10^41.