Okay everyone, it goes deeper!  I tried recompiling the Linux kernel to incorporate a few changes and to see if I could get dmraid to work correctly.  The following is my result:

ubuntu/built-in.o: In function `dm_rh_dec':
/home/erick/Desktop/linux-source-2.6.35/ubuntu/dm-raid4-5/dm-region-hash.c:527: multiple definition of `dm_rh_dec'
drivers/built-in.o:/home/erick/Desktop/linux-source-2.6.35/drivers/md/dm-region-hash.c:535: first defined here
ubuntu/built-in.o: In function `dm_rh_delay':
/home/erick/Desktop/linux-source-2.6.35/ubuntu/dm-raid4-5/dm-region-hash.c:673: multiple definition of `dm_rh_delay'
drivers/built-in.o:/home/erick/Desktop/linux-source-2.6.35/drivers/md/dm-region-hash.c:687: first defined here
ubuntu/built-in.o: In function `dm_rh_recovery_in_flight':
/home/erick/Desktop/linux-source-2.6.35/ubuntu/dm-raid4-5/dm-region-hash.c:661: multiple definition of `dm_rh_recovery_in_flight'
drivers/built-in.o:/home/erick/Desktop/linux-source-2.6.35/drivers/md/dm-region-hash.c:675: first defined here
ubuntu/built-in.o: In function `dm_rh_update_states':
/home/erick/Desktop/linux-source-2.6.35/ubuntu/dm-raid4-5/dm-region-hash.c:431: multiple definition of `dm_rh_update_states'
drivers/built-in.o:/home/erick/Desktop/linux-source-2.6.35/drivers/md/dm-region-hash.c:437: first defined here
ubuntu/built-in.o: In function `dm_rh_start_recovery':
/home/erick/Desktop/linux-source-2.6.35/ubuntu/dm-raid4-5/dm-region-hash.c:707: multiple definition of `dm_rh_start_recovery'
drivers/built-in.o:/home/erick/Desktop/linux-source-2.6.35/drivers/md/dm-region-hash.c:708: first defined here
ubuntu/built-in.o: In function `dm_rh_mark_nosync':
/home/erick/Desktop/linux-source-2.6.35/ubuntu/dm-raid4-5/dm-region-hash.c:393: multiple definition of `dm_rh_mark_nosync'
drivers/built-in.o:/home/erick/Desktop/linux-source-2.6.35/drivers/md/dm-region-hash.c:395: first defined here
ubuntu/built-in.o: In function `dm_region_hash_destroy':
/home/erick/Desktop/linux-source-2.6.35/ubuntu/dm-raid4-5/dm-region-hash.c:230: multiple definition of `dm_region_hash_destroy'
drivers/built-in.o:/home/erick/Desktop/linux-source-2.6.35/drivers/md/dm-region-hash.c:235: first defined here
ubuntu/built-in.o: In function `dm_rh_region_to_sector':
/home/erick/Desktop/linux-source-2.6.35/ubuntu/dm-raid4-5/dm-region-hash.c:118: multiple definition of `dm_rh_region_to_sector'
drivers/built-in.o:/home/erick/Desktop/linux-source-2.6.35/drivers/md/dm-region-hash.c:122: first defined here
ubuntu/built-in.o: In function `dm_rh_dirty_log':
/home/erick/Desktop/linux-source-2.6.35/ubuntu/dm-raid4-5/dm-region-hash.c:255: multiple definition of `dm_rh_dirty_log'
drivers/built-in.o:/home/erick/Desktop/linux-source-2.6.35/drivers/md/dm-region-hash.c:260: first defined here
ubuntu/built-in.o: In function `dm_rh_stop_recovery':
/home/erick/Desktop/linux-source-2.6.35/ubuntu/dm-raid4-5/dm-region-hash.c:697: multiple definition of `dm_rh_stop_recovery'
drivers/built-in.o:/home/erick/Desktop/linux-source-2.6.35/drivers/md/dm-region-hash.c:698: first defined here
ubuntu/built-in.o: In function `dm_rh_bio_to_region':
/home/erick/Desktop/linux-source-2.6.35/ubuntu/dm-raid4-5/dm-region-hash.c:124: multiple definition of `dm_rh_bio_to_region'
drivers/built-in.o:/home/erick/Desktop/linux-source-2.6.35/drivers/md/dm-region-hash.c:128: first defined here
ubuntu/built-in.o: In function `dm_rh_recovery_prepare':
/home/erick/Desktop/linux-source-2.6.35/ubuntu/dm-raid4-5/dm-region-hash.c:604: multiple definition of `dm_rh_recovery_prepare'
drivers/built-in.o:/home/erick/Desktop/linux-source-2.6.35/drivers/md/dm-region-hash.c:619: first defined here
ubuntu/built-in.o: In function `dm_rh_recovery_start':
/home/erick/Desktop/linux-source-2.6.35/ubuntu/dm-raid4-5/dm-region-hash.c:627: multiple definition of `dm_rh_recovery_start'
drivers/built-in.o:/home/erick/Desktop/linux-source-2.6.35/drivers/md/dm-region-hash.c:642: first defined here
ubuntu/built-in.o: In function `dm_rh_flush':
/home/erick/Desktop/linux-source-2.6.35/ubuntu/dm-raid4-5/dm-region-hash.c:667: multiple definition of `dm_rh_flush'
drivers/built-in.o:/home/erick/Desktop/linux-source-2.6.35/drivers/md/dm-region-hash.c:681: first defined here
ubuntu/built-in.o: In function `dm_rh_region_context':
/home/erick/Desktop/linux-source-2.6.35/ubuntu/dm-raid4-5/dm-region-hash.c:130: multiple definition of `dm_rh_region_context'
drivers/built-in.o:/home/erick/Desktop/linux-source-2.6.35/drivers/md/dm-region-hash.c:134: first defined here
ubuntu/built-in.o: In function `dm_region_hash_create':
/home/erick/Desktop/linux-source-2.6.35/ubuntu/dm-raid4-5/dm-region-hash.c:163: multiple definition of `dm_region_hash_create'
drivers/built-in.o:/home/erick/Desktop/linux-source-2.6.35/drivers/md/dm-region-hash.c:167: first defined here
ubuntu/built-in.o: In function `dm_rh_get_region_key':
/home/erick/Desktop/linux-source-2.6.35/ubuntu/dm-raid4-5/dm-region-hash.c:136: multiple definition of `dm_rh_get_region_key'
drivers/built-in.o:/home/erick/Desktop/linux-source-2.6.35/drivers/md/dm-region-hash.c:140: first defined here
ubuntu/built-in.o: In function `dm_rh_inc_pending':
/home/erick/Desktop/linux-source-2.6.35/ubuntu/dm-raid4-5/dm-region-hash.c:518: multiple definition of `dm_rh_inc_pending'
drivers/built-in.o:/home/erick/Desktop/linux-source-2.6.35/drivers/md/dm-region-hash.c:523: first defined here
ubuntu/built-in.o: In function `dm_rh_get_state':
/home/erick/Desktop/linux-source-2.6.35/ubuntu/dm-raid4-5/dm-region-hash.c:333: multiple definition of `dm_rh_get_state'
drivers/built-in.o:/home/erick/Desktop/linux-source-2.6.35/drivers/md/dm-region-hash.c:338: first defined here
ubuntu/built-in.o: In function `dm_rh_get_region_size':
/home/erick/Desktop/linux-source-2.6.35/ubuntu/dm-raid4-5/dm-region-hash.c:142: multiple definition of `dm_rh_get_region_size'
drivers/built-in.o:/home/erick/Desktop/linux-source-2.6.35/drivers/md/dm-region-hash.c:146: first defined here
ubuntu/built-in.o: In function `dm_rh_recovery_end':
/home/erick/Desktop/linux-source-2.6.35/ubuntu/dm-raid4-5/dm-region-hash.c:643: multiple definition of `dm_rh_recovery_end'
drivers/built-in.o:/home/erick/Desktop/linux-source-2.6.35/drivers/md/dm-region-hash.c:658: first defined here
make: *** [vmlinux.o] Error 1

There is officially a problem with the dm-raid4-5 module in the Linux kernel.