What is the ruling on one who vowed to donate money or pray a certain number of rak'ahs upon success, but then forgot the exact amount or specific number, while remembering the minimum or an approximation of the quantity? And is expiation possible for this?

First, we point out the reprehensibility of a conditional vow, even though fulfilling it becomes obligatory if the condition is met. As for the charity or prayer you vowed, the exact amount of which you do not know, you are obligated to strive and investigate to ascertain its measure. If you are unable to do so, then you are obligated to pray and give charity in an amount that ensures the discharge of your responsibility with certainty or with strong presumption.