Okay, we are tasked with adding 1580 and 9529. Let's begin!

Step 1: We'll start by adding the digits 0 & 9 in column 1 and get 9.

Step 2: We'll start by adding the digits 8 & 2 in column 2 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 5 & 5 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 1 & 9 in column 4 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

So, 1580 + 9529 = 11109.

