Scenario – The Gold Hunt

You recently introduced a new scenario in the game—to meet the expenses of his army, Sir Foo is out on a mission to collect gold from a recently acquired territory. The scenario starts with Sir Foo arriving at a place full of gold coins, jewelry, and so on. There are a couple of problems though. Firstly, the gold is scattered all over the field. Secondly, Sir Foo doesn't have time to collect all the gold on the field.

What you see behind Sir Foo is an imaginary gold field. Sir Foo will enter from the left side and travel across the field. He will only collect the coins lying along his path and ignore all the remaining gold scattered across the field.

Let's represent this gold field as a circle with a radius of nearly 10 miles (diameter of 20 miles), and center located at coordinates x = 0 and y = 0, as shown in the following screenshot:

Observe the following screenshot. The dotted line (the diameter of the field) shows the path that Sir Foo traverses on his...