Actually I do a lot of integrals this way – symbolically but checking whether the transformation was legit evaluating definite integral on few random intervals. For me is very helpful and I believe it can be extended to problems beyond integrals.
It never occurred to me before, but running simulations and looking up the result in a dictionary of constants might be a helpful learning approach for people who are more adept at going from practice to theory.
How many fromblaz of size N are there? lets count them for N=1 ... N=8 or whatever is tractable to count using naive methods then hope a useful result shows up in OEIS.
OEIS will also return equations for simple linear integer expressions without an OEIS entry.
Unfortunately, the tools for single constants are significantly less good than OEIS.