Let $f(x) = x - \lfloor \sqrt{x} \rfloor^2$. What is $f(101) + f(102) + f(103) + \cdots + f(110)$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $f(x) = x - \lfloor \sqrt{x} \rfloor^2$. What is $f(101) + f(102) + f(103) + \cdots + f(110)$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
55
Let $f(x) = x - \lfloor \sqrt{x} \rfloor^2$. What is $f(101) + f(102) + f(103) + \cdots + f(110)$?
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