Okay, we are tasked with adding 3577 and 3603. Let's begin!

Step 1: We'll start by adding the digits 7 & 3 in column 1 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 7 & 0 in column 2 and get 8.

Step 3: We'll start by adding the digits 5 & 6 in column 3 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 3 & 3 in column 4 and get 7.

So, 3577 + 3603 = 7180.

