"You can count on me": 任せて

Soundtrack: Junior Kimbrough's All Night Long
任せる 【まかせる】 (v1,vt) (1) to entrust (e.g. a task) to another; to leave to; (2) to passively leave to someone else's facilities
I'm constantly trying to directly translate my English thoughts and speaking style into Japanese. This is 1.) ill-advised 2.) near impossible. For example, I use "no problem" alot in English, which directly translates into "問題ない”but sounds very unnatural when used in similar context to the English "no problem." The more direct translation of "問題ない” is that "no problem exists." A friend of mine suggested using "任せて" which, when dissected, means ”obligation entrusted to me” or more naturally "you can count on me."