When you define a function using a sum or integral, the calculator often gives the error “You can’t use ‘{variable}’ as an index because it’s already defined.” (for sums) or “You can’t use ‘{variable}’ as an integration variable because it’s already defined.” (for integrals) when you plug the function into a function which uses the same indexing/integration variable. Most notably this happens when you plug a function into itself. In essence, Desmos does not properly handle alpha conversion.

Here’s the link demonstrating several instances of this issue: https://www.desmos.com/calculator/x7zhgehtqu. Additionally, if you remove the backslash from the g(g(x)) line, the calculator becomes unresponsive until the page is refreshed in the sense that nothing will be computed if you change/add equations or move the window.