Do composers need to write the music for every instrument individually or is there some other trick?

Quoth panamajack:

Other brass instruments may not use them as much, but we do have alternate fingerings for many notes. For instance, F (on an instrument based on the B flat scale) can be open or 13, and 3 by itself is equivalent to 12 (and on a four-valve instrument, 4 is usually equivalent to 13). I was never all that great a performer, but one thing I excelled at was the alternate fingerings, since I was somehow always ending up with the tuba with the sticky valves.