In the modern benoni, what should I do if this happens? Let's say the position looks like this:

[Title "Black to move"]
[FEN ""]

 1.d4 Nf6 2. c4 c5 dxc5


I usually do this:

[Title "Black to move"]
[FEN ""]

1.d4 Nf6 2. c4 c5 3. dxc5 e6 4. b4 a5


I have played this position only once, and won, but still this might repeat in a open tournament I might go soon, so I need help to figure this out, because in the videos I have seen for the Benoni, I can't really find this variation anywhere.
In the modern benoni, what should I do if this happens


Your continuation is the strongest in my opinion. I would advise you not to change anything.


  because in the videos I have seen for the Benoni, I can't really find this variation anywhere.


Of course, because it is weak. The best White can do after your move, in my opinion is this:

[Title "BenOni"]
[fen ""]

1.d4 Nf6 2.c4 c5 3.dxc5 e6 4.b4 a5! 5.b5 Bxc5 


Here, I would aim for Bb2 + e3 + Nf3 + Be2 setup as White. Not ideal, but surely playable and the nearest towards equality I can get after that horrible b4...

If White tries to be "smart" about keeping the extra pawn, here is how I would play as Black:

[Title "BenOni"]
[fen ""]

1.d4 Nf6 2.c4 c5 3.dxc5 e6 4.b4 a5! $40 5.Bd2 ( 5.Qb3 axb4! 6.Qxb4 Na6! ) ( 5.Qa4 Na6! 6.a3? ( 6.Bd2? axb4 7.Bxb4 Nxb4! 8.Qxa8 Nc2+ 9.Kd2 Nxa1 $17 ) 6...axb4! $17 7.axb4?? Nc7! $19 ) 5...axb4! 6.Bxb4 Na6! $32 $40 7.Ba3 Nxc5 8.Bb2!? ( 8.Nf3? Rxa3! 9.Nxa3 Qa5+ 10.Qd2 Qxa3 $17)


Your only problem after b5 will be that you must play ...d5 which turns the game into positional battle. There will be no wild tactical positions anymore ( but still you will stand better ) so you will have to adapt psychologically to this fact ( tactical players hate "dry" positions and positional ones hate "wild" positions ). Try not to fall for this psychological trick. That is my last advice and a warning.

Good luck on the tournament!