Sometimes if we are going to use a particular set of operations frequently, it can be useful to give that set of operations an abbreviated symbol to stand for the whole.

For example, if we define \( \uparrow \) to mean \( \uparrow x = x^2 + 1 \), then what is the value of \( \uparrow 10 + \uparrow 3 \)?

Given the definition, \( \uparrow 10 + \uparrow 3 = ((10)^2 + 1) + ((3^2) + 1 ) = 111 \).

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