You Do Need power plug adapter while traveling from Turkmenistan to Anguilla.

Here is Why You Need An Adapter

The outlet and plug type used in Anguilla are A and B and in Turkmenistan are C and F. This is how they look like.

Turkmenistan

In Turkmenistan, outlets of type C and F are in use.

Type C

Type F

Anguilla

In Anguilla, outlets of type A and B are in use.

Type A

Type B