Sift the flour, baking powder, soda, pumpkin pie spice and salt together; set aside. Beat the eggs until fluffy; add the sugars. Beat until very thick. Stir in the pumpkin and oil, until smooth. Blend flour mixture thoroughly into the creamed mixture. Pour into a greased and floured 10" tube pan or bundt pan. Bake in preheated 350 degree oven for about one hour or until cake tester inserted near the center comes out clean. Cool for 10 minutes before removing from the pan. Cool completely on a wire rack.
Frosting:
In the bowl of an electric mixer, cream the cream cheese and butter on low speed until smooth. Stir in the maple syrup and vanilla extract. With the mixer still on low, slowly add the confectioners' sugar and mix until smooth.