The Mayan Calendar first appeared as a cylinder piece of stone with a bunch of carved art on it. In the very middle is a face with a tongue sticking out, based off of the real Mayan Calendar from real life. Dinosaur heads, circles and triangles appear near the edges as well with unique designs.
In Food Orb 3, it first appeared in an area on a shelf inside the Mayan Temple. Evil Donut was seen near it, and decided to end the world with it, because the Mayan Calendar in real life was once built to mark the date of where the world was predicted it would end (2012). Evil Donut came to Evil Cookie and Evil Pizza and said that Evil Donut found the artifact and that they could end the world with it. However, near the ending, Evil Donut and DeliciousBakedPie were seen near the machine that could end the world. They were fighting over the Mayan Calendar, and after that scene, DeliciousBakedPie broke the Mayan Calendar, and Evil Donut, along with Evil Pizza and Evil Cookie chase DeliciousBakedPie out of the tunnel. To learn more about the Mayan Calendar in real life, here.