well, they can probably put out over 10000Amps for a short period of time...its called a "short" hehe
some manufacturers do provide a "Peak Discharge Current" spec, the problem with this is what constitutes a "peak" unit of time.
I would never think of 30seconds as a small unit of time when it comes to electrical loads, maybe 2seconds, but not 30.
If you need to have a large "burst" capacity consider using some supercapacitors in parallel, they are great for that!!