まい

Meanings

Auxiliary verb probably not; probably won't; probably doesn't; probably isn't
intend not to; will not
trying not to; attempting not to (as ～とする)
whether you ... or not; whether one does ... or not (as ...（よ）うが...～が or ...（よ）うと...～と)
couldn't you?; won't you?; how about? (as ～か; indicates request or invitation) See also: 真烏賊 (マイカ). See also: 佳 (か).
it's not as if ..., so; it's not like; it's not as though (as（では／でも）ある～し)
would surely not ... (if); would never ... (and yet) (as（ある）～に; indicates counterfactuality)
surely not; there's no way that (as（では／でも）ある～に; indicates reproach; oft. at sentence end)
must not; don't; shall not (indicates prohibition; oft. as ～ぞ)

君が行こうと行くまいがそんなことは、たいしたことではない。
It makes no difference whether you go or not.
君がそれを信じようと信じまいと僕にはどうでも良い。
It makes no difference to me whether you believe it or not.
君がそれを信じようと信じまいと僕にはたいした違いはない。
It makes little difference to me whether you believe it or not.
気に入ろうが入るまいが、君は行かねばならない。
Whether you like it or not, you have to go.
火星へ旅行できる日も遠くはあるまい。
It won't be long before we can travel to Mars.

And 5 more.