komponi

One root, not two. Kompon- looks as though it ought to be a prefix plus something, and it is not: Esperanto has no root pon-, so komponi arrives whole from Latin componere and stays whole. The same is true of inspiri and deponi, which sit in the same band and carry the same buried Latin joinery.

It means music, and verki means everything else. This is the fence to learn. You verkas a book, an article, a poem or a report: verki is to author a work. You komponas a symphony, a song or a score. The two overlap only in translation, never in Esperanto, and writing li verkis simfonion marks you out immediately. A composer is a komponisto, a piece is a komponaĵo.

Two neighbours that are not it. Komponi in the wider sense of putting parts together does exist in technical prose, but everyday Esperanto uses kunmeti for that and keeps komponi for music. And the printer's word is komposti, to set type, with kompostisto for the compositor: a different root that differs by one consonant and is worth noticing once so you never confuse the two.