What is the ruling on the seven hundred and fifty riyals I took for brokerage without my friend's knowledge, given his satisfaction with the agreed-upon profit?

It is not permissible to take a commission on your friend's profit without his knowledge, as it is a type of ju'ala (commission/fee for a service) and is not valid unless the payer is aware of it. Furthermore, a transaction with a known profit and a specified term is not valid unless it is conducted in a Shariah-compliant manner, such as a murabaha (cost-plus sale). As for partnership (sharika) and mudaraba (profit-sharing partnership), they are not valid if the capital or the profit is guaranteed.