The operation ⊗ is defined on the set of positive integers by the rule \(a⊗b = a+b^2\). What is the value of \((4⊗3)⊗5\) ?

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Following the rule \(a⊗b = a+b^2\):

$$ (4⊗3)⊗5 $$ $$ =(4+3^2)⊗5 $$ $$ =13 ⊗ 5 $$ $$ =13+5^2 $$ $$ = \boxed{38} $$