The computer has a table in memory that tells it S^6(0) = 6 (or equivalently O O O O O O = 6 apples). When it sees a symbol - for example S^6(0) - it searches this table for the same symbol, and then outputs the corresponding number. In no stage of this process does the computer "calculate" anything - it doesn't even need to know that S^5(0)=5 in order to find that S^6(0)=6. In fact S^5 might not even be in the table.
You cannot calculate S^(x+1)(0) before the result of S^x(0) is known.
To calculate S^6(0) you start by calculating S(0) ----> It's not possible to "identify S^6(0) with 6" if you haven't calculated S(0) first, because you cannot know S^6(0) at this point.