-12
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The biggest integer "between" -9 and -3 is -4.
There are eight of them.
9
The square of 3 is 9, which does not lie between consecutive integers. Perhaps you mean the square root of 3, which lies between 1 and 2.
The positive integers between 4 and 9 inclusive are 4, 5, 6, 7, 8, 9.