solution: Points with integer coordinates are called lattice points. The length of the rectangle is $5 - (-5) = 10$ units. There will be 9 lattice positions between the two vertical sides of the rectangle. The height of the rectangle is $4 - (-4) = 8$ units. There will be 7 lattice positions between the top and bottom of the rectangle. That's a total of $9 \times 7 = \boxed{63}$ lattice points.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  Consider the rectangle with vertices at $(5,4),$ $(5,-4),$ $(-5,4),$ $(-5,-4)$. How many integer coordinates will be strictly inside the rectangular region?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 63
extra_info.question: Consider the rectangle with vertices at $(5,4),$ $(5,-4),$ $(-5,4),$ $(-5,-4)$. How many integer coordinates will be strictly inside the rectangular region?
extra_info.split: test