There's an app called iCAB that ALMOST did it - but it did not work for me, as far as I know , this is the only option if you want to upload files aside from camera roll using web browser.I find this very odd. I've used the document picker to upload files of various types and from various sources (including Dropbox, Devonthink, iCloud Drive etc) on any number of websites for a good while now. I'm tempted to think it might be the fault of the page! Did you try reloading as desktop?
Exporting a file from iBooks is something else. I agree it should be possible for files which are created rather than bought, but at the same time, iBooks isn't intended as a storage container and there's any number of alternatives which do allow uploading at will.
It may or may not be Moodle sites specific - and many university use them. But I have no idea, and have no time to figure this out. Im busy trying to figure out poor file system of iOS and Back up options without iCLOUD
edit : I just uploaded to government site and it was good - so def. site specific but I was able to only upload jpg but ok.
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