Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking pan with cooking spray.
Combine flour, baking soda, baking powder, cinnamon, and salt in a bowl. Add yogurt, carrot pulp, milk, maple syrup, apple pulp, dates, and egg. Mix with a wooden spoon until batter is blended and thick.
Spread batter in the prepared baking pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 30 to 35 minutes.