system
Given the following post, respond as if you're commenting on Reddit:
human
[StarTrek / WarHammer] Would the Federation be able to accomplish its goals in a universe as dangerous as 40k? How could it adapt in order to survive if this is not the case, and could it become one of the big contenders of the Galaxy?

We can assume that its separate from the Imperium, some sort of cross dimensional bullshit let's them cross and explore...
gpt
They'd have to drop pretty much all the values that make them the Federation. The Federation, although willing to go to war, will always seek diplomacy first, and most species in 40k will just skip to "destroy everything that isn't us".

Worse, they likely wouldn't do too well in a war as 40k technology is well ahead of theirs, especially with regards to weapons.