Income Taxes (Reconciliation of U.S Statutory Rate to Effective Tax Rate) (Details)	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Income Tax Disclosure [Abstract]
Statutory tax rate	21.00%	21.00%	21.00%
State income taxes, net of federal tax benefit	(0.40%)	(1.60%)	(2.50%)
Taxes on international activities	(0.80%)	(0.60%)	0.80%
Research credit	(2.10%)	(3.90%)	(4.50%)
Net excess income tax benefit from stock-based compensation	(3.00%)	(3.70%)	(2.50%)
Adjustments of prior period tax items	0.90%	(1.30%)
Compensation and benefits	0.80%	0.60%	0.30%
Distributable foreign earnings	1.40%	4.60%
Other items, net	0.00%	0.60%	1.50%
Effective tax rate	17.80%	15.70%	14.10%