Okay, we are tasked with adding 6541 and 3013. Let's begin!

Step 1: We'll start by adding the digits 1 & 3 in column 1 and get 4.

Step 2: We'll start by adding the digits 4 & 1 in column 2 and get 5.

Step 3: We'll start by adding the digits 5 & 0 in column 3 and get 5.

Step 4: We'll start by adding the digits 6 & 3 in column 4 and get 9.

So, 6541 + 3013 = 9554.

