Starbase 413 was a Federation starbase in Starfleet's use in the 24th century, located somewhere in the galaxy's Alpha or Beta Quadrant.
History and specifics[]
In the year 2368, the crew of the USS Enterprise turned over Kila Marr to Starfleet authorities on Starbase 413 after she destroyed the Crystalline Entity. (SCE - What's Past eBook: Many Splendors)
Following the return of the USS Enterprise from the year 2063, the Enterprise spent a month docked at Starbase 413, where the Borg technology was removed from the starship. (TNG - The Dominion War novel: Behind Enemy Lines)
In 2376, the USS da Vinci was to visit Starbase 413 to collect mining equipment and then head to Beta Argola. (SCE eBooks: Here There Be Monsters, Ambush)