For use with Duolingo En→Ja and Ja→En courses: Automatically toggles your Japanese IME on/off based on whether you need to translate the sentence into English or Japanese. ^^
!! Important !! Chrome and Opera users will need to enable the "Experimental Web Platform Features" browser flag for this userscript to work at all. I'm using the "inputmode" experimental HTML attribute from this to make the IME toggling work.
To enable this flag, simply copy and paste the line below into your address bar and it'll take you to the exact setting you need to turn on:
Firefox users won't need to do anything like this, as Firefox instead has a different feature I'm using and it's enabled by default. ^^