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)