solution: Let $m$ be the least possible number of leaves. Then $2m$ is the least possible number of pages. We know that $2m\equiv 3\pmod 7\implies 8m \equiv 3\cdot 4\pmod 7\implies m\equiv 12\equiv 5\pmod 7$. So $m=5+7a$ for some positive integer $a$. The smallest such number greater than $100$ is $5+7\cdot 14=\boxed{103}$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  A book is said to have $n$ leaves if it is composed of $n$ pieces of paper. On the other hand, the number of pages is twice the number of leaves because each side of a piece of paper is defined as a page.
  
  If the number of pages in a book is $3$ more than a multiple of $7$, and the number of leaves is greater than $100$, then what is the smallest possible number of leaves?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 103
extra_info.question: A book is said to have $n$ leaves if it is composed of $n$ pieces of paper. On the other hand, the number of pages is twice the number of leaves because each side of a piece of paper is defined as a page.
  
  If the number of pages in a book is $3$ more than a multiple of $7$, and the number of leaves is greater than $100$, then what is the smallest possible number of leaves?
extra_info.split: test