To find the quotient of \(-1011\) divided by \(-25\), you can perform the division as follows:
\[ \frac{-1011}{-25} = \frac{1011}{25} \]
Now, dividing \(1011\) by \(25\):
\[ 1011 \div 25 = 40.44 \]
Since you are looking for the quotient in terms of integer division (the whole number part), you take the integer part of \(40.44\), which is \(40\).
Thus, the quotient when you divide \(-1011\) by \(-25\) is:
\[ \boxed{40} \]