As those of you who have been participants in the integration debates over the last few days (see here, for example) may know, we have been essentially debating over the nature of the content we expect here at Math.SE.
To summarize, there are users (whom I will not name, and the one in the link is not the only one) who post answers free from context, demonstration, proof, origin, or reference. One user told me that (s)he will just continue to post Maple output because Maple clearly can do everything a human can do, but better. Another user posts beautiful formulae as answers to requests to show how this or that integral/sum/complicated expression may be evaluated in closed form, but the formulae only, without comment.
(Actually, that latter user chose to respond to requests for context by issuing the teenage-wiseass claim that he was merely stating axioms that do not require proof. Hardee-har-har.)
What to make of this? Technically, in a Q & A site, if the OP asks, "Is there a closed-form expression for this integral?" and a poster just says "Yes," then the question has been answered. If the OP asks further, "what is that value," and the poster then plops down a formula and nothing else, then that should also work. The fact that there are any upvotes means that the answer is useful to someone.
But could one of those people explain to me how on earth such an answer is useful?
Look, if all I care about is an answer, then, yeah, Maple and/or Mathematica will do in many cases. And if they can't do it, then I can evaluate things numerically. These black boxes have the whole thing covered. In fact, in a TED talk, Conrad Wolfram stated that we should change the way we teach mathematics to schoolkids because nobody is really interested in the mechanics behind computation anymore.
A personal story you may skip if you are tiring of me by now. In my previous life, I used to write software that simulates complex lithographic processes. Users of the software became trained to just trust the output of the software. Thus, when their models did not conform with their experiments, they spent a lot of valuable time in the fab checking experimental conditions, interrogating tool vendors, etc. Nobody thought to police the software vendors; this eventually became my job, because I was the only one who would design cases that could be solved analytically and demonstrate the inaccuracies in other vendors' software. Without skills needed in evaluating integrals, sums, etc., who will "watch the watchers"?
[And by the way, ponder this: how many of you can do long division on paper, quickly and accurately?]
So, I come to my point: is this a Mathematics site, where we expect folks to provide methodology and reason along with a result, or is this a Q & A site where we are OK with results plopped down from the heavens? My "not an answer" flags have been declined because some people find such answers useful. But why? How on earth is a contextless number or formula useful to anyone?