"I will go to the supermarket to buy bananas."
Then, you are saying "I want to go to the supermarket to buy bananas". If you replace 会 with 要
Here 会 means a future plan; You say it to let the speaker know where to expect you or to hear if the speaker might want you to buy some other things.
要 would mean that you have a necessity to go, e.g. you are making banana bread but there is no banana in your house. Possible scenarios are
- the speaker wanted you to do some other things and by this you tell the speaker that you are occupied.
- you follow with a request to the speaker to do something for you while you are out
- you follow with a request to borrow the speaker's car