here are two that I've been pondering:

1) "it's the absolute opposite of a no-brainer" - given that a no-brainer is defined (by M-W) as something that requires a minimum of thought, what would the exact opposite word be?

2) consider the lyric for I’ll Do Anything by Jason Mraz:
“We can cool in the gang if you’d rather hang
Ain’t no thing. I can be lucubrious with you.”

Urban Dictionary suggests calm, cool, relaxed; the closest Latin root I can find is lūcubrāre , to work by artificial light [cf. lucubrate] - what's going on here?

2a) or is it related more to luculent, clear in thought or expression: lucid