I think 勉強 and 学ぶ are nearly same, then they are exchangeable.
But not completely equal. In addition, I have a image on 勉強 is done with stress.
On your example, you are doing homework and homework is given by teacher and may have to been done until tomorrow. Then I understand that study is suitable in this case.
I realized that I don’t write this. “I feel that study is 勉強, and learn is 学び (or 学習).”
It is the same as the previous answer by Paola Seminara.
There is also such examples.
In this case,
「今回の仕事はいい学びになった」 I feel something wrong.