You can execute anonymous apex using Jetstream, just like the developer console, but with a much better code editor and log viewing experience.
Enter in your apex and press Submit (or ctrl/cmd+enter) to execute the apex and see the results on the right-hand side of the page.
Changing the log levels will determine how much detail is returned in the log from Salesforce.
Each time you execute, Jetstream will save the apex in your history so you can easily recall it and execute the code again.
You can search the results using the built-in filter and can also toggle to only show the debug statements from the log.