I know: $$\int_0^1 x^{-x} dx = \sum_1^\infty k^{-k}.$$
I think this is startling and neat at the same time that it has a superficial 'obviousness.' (Though the proof is interesting.) I'm just looking for a search term that would get me to sources discussing these types of relations, and it's hard to ask questions in person during the lockdown. Thanks.