Belt of Giant's Strength with Manual of Gainful Exercise

Question

Suppose your STR score is 8 but you attune to a belt of storm giant strength (your STR becomes 29). You then use a manual of gainful exercise (+1 to STR and maximum STR). What is your current STR score? What is your STR score, as well as your maximum STR score, if you remove the belt?

Answer 1

Belt of Giant Strength

While wearing this belt, your Strength score changes to a score granted by the belt. If your Strength is already equal to or greater than the belt's score, the item has no effect on you

(emphasis added)

Manual of Gainful Exercise

If you spend 48 hours over a period of 6 days or fewer studying the book's contents and practicing its guidelines, your Strength score increases by 2, as does your maximum for that score

Combining the items

Looking at the difference in wording, it's clear that the Manual provides a permanent bonus to your strength - there are no conditions to it. So your strength score would change to a 10, with the maximum changed to 22.

The belt has a condition (you have to be wearing it), and when it is met your score changes to 29. It's not a bonus (e.g. +17), it's a replacement. Whatever your strength score beforehand, if your strength is less than 29 it is becomes 29. The strength gain from the manual still doesn't bring you above 29, so it wouldn't change the belt's effect.

Answer 2

29

Belt of Giant's Strength

While wearing this belt, your Strength score changes to a score granted by the belt. If your Strength is already equal to or greater than the belt’s score, the item has no effect on you.

emphasis mine

While wearing the belt your strength becomes 29 while wearing it only unless it is already greater than that. All the item does is set your strength. Any attempts to modify it fail unless it puts your natural STR above 29. At which point the belt fails to help you at all.

Manual of Gainful Exercise

If you spend 48 hours over a period of 6 days or fewer studying the book's contents and practicing its guidelines, your Strength score increases by 2, as does your maximum for that score

As far as your natural STR maximum, it would be 22 after the Manual of Gainful Exercise, but this would have no bearing on your stats while wearing the belt.