To make the flax eggs, combine the flax meal and water in a small bowl and mix well. Set aside for 10 minutes to gel.
In a large bowl, combine the oats, quinoa, baking powder, salt, maple syrup, coconut oil, vanilla, flax eggs, and bananas, and mix until well-combined.
Divide the base dough equally between 4 medium bowls.
Add the peanut butter and chocolate chips to 1 bowl and mix until combined.
Add the apple, walnuts, cinnamon, and nutmeg to another bowl and mix until combined.
Add the carrots, cinnamon, nutmeg, and almond butter to another bowl and mix until combined.
Add the almond butter, strawberries, raspberries, and blueberries to the last bowl and mix until combined.
Grease 2 9x13-inch (23x33-cm) baking pans with nonstick spray. Transfer the bar mixtures to the pans, packing each mixture into half of a pan with a spoon or spatula.
Bake for 25-30 minutes, until the edges are slightly golden brown.
Remove the pans from the oven and let the bars cool for 20 minutes, then refrigerate for at least 30 minutes, or up to 5 days. Gently cut each flavor into 6 bars, then remove from the pans with a spatula.