Using F#, write a function repeat_map : ('a -> 'a) -> 'a list -> 'a list such that repeat_map f xs applies f once to the first element of xs, twice to the second, three times to the third, and so on.

Tests for the function:

repeat_map (fun x -> x + 1) [0..10];; // Should return [1; 3; 5; 7; 9; 11; 13; 15; 17; 19; 21]

repeat_map (fun x -> - x) [1..10];; // Should return [-1; 2; -3; 4; -5; 6; -7; 8; -9; 10]

repeat_map (fun x -> x + x) ["x"; "y"; "z"; "w"];; // Should return ["xx"; "yyyy"; "zzzzzzzz"; "wwwwwwwwwwwwwwww"]