Is it permissible to take profits resulting from an amount deposited in an investment account with a bank that operates according to Islamic Sharia, while there is doubt about how these profits are calculated?

It is not possible to rule whether the amounts added by the bank are permissible (halal) or impermissible (haram) without knowing the method of transaction or the contract concluded. The bank's claim of operating according to Sharia requires proof. It is permissible to take these amounts because the default for contracts among Muslims is validity until proven otherwise.