Okay, so I need to evaluate this expression: the ceiling of (3.6 squared) minus the ceiling of 3.6 squared. Let me break this down step by step. First, I should remember what the ceiling function does. The ceiling of a number is the smallest integer that is greater than or equal to that number. So, for example, the ceiling of 3.2 is 4, and the ceiling of 5 is 5. Got it.

Let me tackle the first part of the expression: the ceiling of (3.6 squared). Let me compute 3.6 squared first. 3.6 times 3.6. Hmm, 3 times 3 is 9, 3 times 0.6 is 1.8, 0.6 times 3 is another 1.8, and 0.6 times 0.6 is 0.36. Adding those up: 9 + 1.8 + 1.8 + 0.36. Let's see, 9 + 1.8 is 10.8, plus another 1.8 is 12.6, plus 0.36 is 12.96. So 3.6 squared is 12.96. Then, the ceiling of 12.96. Since 12.96 is between 12 and 13, the ceiling would be 13. Okay, so the first part is 13.

Now the second part: (the ceiling of 3.6) squared. The ceiling of 3.6 is 4, right? Because 3.6 is between 3 and 4, so the smallest integer greater than or equal to 3.6 is 4. Then, 4 squared is 16. So the second part is 16.

Putting it all together: 13 - 16. That equals -3. Wait, that seems negative. But let me check my steps again to make sure I didn't make a mistake.

First, 3.6 squared is 12.96. Ceiling of that is 13. Correct. Ceiling of 3.6 is 4, squared is 16. 13 minus 16 is indeed -3. Hmm, but is that possible? The problem is just asking for the evaluation, so maybe negative numbers are allowed here. Let me verify once more.

Alternatively, maybe I messed up the order of operations? Let me check the original expression again: ceiling of (3.6 squared) minus (ceiling of 3.6) squared. So the parentheses make it clear that each ceiling is applied to the respective operation. So yes, first compute 3.6 squared, then take ceiling, then compute ceiling of 3.6, then square it, then subtract. So the steps are correct. Therefore, the answer is -3. That seems straightforward. But wait, maybe I should check if there's a different interpretation. For example, if someone misapplies the ceiling function, but no, the notation is clear.

Alternatively, maybe the question is trying to test properties of the ceiling function. Let me recall that the ceiling function is non-decreasing, so if a number increases, its ceiling doesn't decrease. But in this case, we have 3.6 squared, which is 12.96, and 3.6 is 3.6. The ceiling of 3.6 is 4, but 4 squared is 16, which is significantly larger than the ceiling of 12.96. Hence, the difference is negative. That makes sense.

Alternatively, maybe there's a typo in the problem, but as per the given, it's correct. So I think the answer is -3.

Wait, but let me think again. Let me verify the arithmetic. 3.6 squared. 3.6 times 3.6. Let me compute this again step by step. 3 times 3 is 9, 3 times 0.6 is 1.8, 0.6 times 3 is 1.8, 0.6 times 0.6 is 0.36. Adding them up: 9 + 1.8 + 1.8 + 0.36. 9 + 1.8 is 10.8, plus 1.8 is 12.6, plus 0.36 is 12.96. Correct. So ceiling is 13. Then ceiling of 3.6 is 4, squared is 16. 13 - 16 is -3. Yes, that's correct. So the answer is -3. I think that's solid. Maybe I was overcomplicating, but I can't see any mistakes here. So final answer is -3.
Therefore, the final answer is $\boxed{-3}$.
</think>