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If you have a subscription and have created a feature service, you currently can export the data. This is done from the item details page of the feature service.
Thank you Mike.
We are currently participating in the Arcgis for Organizations trial, and based on your hints I've now found the places to create and export Feature Services. (For those that follow, the export options are CSV and shapefile.)
I guess that as we created this account and site before the trial started we're stuck with web maps and imprisoned data for this project. 😕
((Cross-post thread: http://gis.stackexchange.com/questions/28291/arcgis-online-content-as-georss-or-geojson/))
To add to the above, only the Feature Service Owner or a user with Admin rights on the ArcGIS Online for Organizations site can export the data.
Do you know if this is still the case? Is there documentation of this somewhere?
Useful discussion, but I am running into the same issue, it it possible to extract data while using the trial version for arcgis online?