Datasets:

tuan3110
/

University-HMER-RealClassroom

sample_id stringlengths 8 8	latex stringlengths 61 168	category stringclasses 5 values	source stringclasses 1 value	token_count int64 26 66	severity stringclasses 3 values	width int64 690 768	height int64 82 110	split stringclasses 1 value
S001-I01	\int _ { 1 } ^ { 6 } \cos y + \sqrt { t ^ { 2 } + 4 } + u \cdot m ^ { 2 } d y	integral	real_classroom_camscanner_original	32	normal_26_40	765	109	train
S001-I02	\int _ { 2 } ^ { 7 } \frac { t ^ { 4 } } { t + 3 } + \theta u + \log ( v + 8 ) + n ^ { 5 } + \log k + \frac { m ^ { 4 } } { m + 2 } d t	integral	real_classroom_camscanner_original	57	stress_56_80	765	109	train
S001-I03	\int _ { 3 } ^ { 8 } \sqrt { u ^ { 2 } + 4 } + \frac { 6 v } { v + 7 } d u	integral	real_classroom_camscanner_original	32	normal_26_40	765	109	train
S001-I05	\int _ { 1 } ^ { 5 } \frac { 6 x } { x + 7 } + \log ( k + 8 ) d x	integral	real_classroom_camscanner_original	28	normal_26_40	765	109	train
S001-I06	\int _ { 2 } ^ { 6 } y \cdot m ^ { 2 } + m ^ { 5 } + \sqrt { a ^ { 2 } + 3 } + \alpha b + \frac { 5 x } { x + 6 } d y	integral	real_classroom_camscanner_original	49	long_41_55	765	109	train
S001-I07	\int _ { 3 } ^ { 7 } \log ( t + 8 ) + \log a + \alpha b + \frac { 5 x } { x + 6 } d t	integral	real_classroom_camscanner_original	34	normal_26_40	765	109	train
S001-I08	\int _ { 0 } ^ { 8 } u ^ { 5 } + \frac { b ^ { 4 } } { b + 2 } + \frac { 5 x } { x + 6 } d u	integral	real_classroom_camscanner_original	41	long_41_55	765	109	train
S001-I09	\int _ { 1 } ^ { 9 } \log v + \sqrt { x ^ { 2 } + 3 } + y \cdot n ^ { 2 } + \tan ( t + 7 ) + u ^ { 3 } d v	integral	real_classroom_camscanner_original	45	long_41_55	765	108	train
S001-I10	\int _ { 2 } ^ { 5 } \frac { x ^ { 4 } } { x + 2 } + \alpha y + \tan ( t + 7 ) + u ^ { 3 } + \tan v + \frac { n ^ { 4 } } { n + 1 } d x	integral	real_classroom_camscanner_original	57	stress_56_80	765	109	train
S002-I01	\int _ { 3 } ^ { 6 } \sqrt { y ^ { 2 } + 3 } + \frac { 5 t } { t + 6 } d y	integral	real_classroom_camscanner_original	32	normal_26_40	750	107	train
S002-I02	\int _ { 0 } ^ { 7 } \alpha t + u \cdot n ^ { 2 } + \tan v + \frac { n ^ { 4 } } { n + 1 } d t	integral	real_classroom_camscanner_original	38	normal_26_40	750	107	train
S002-I03	\int _ { 1 } ^ { 8 } \frac { 5 u } { u + 6 } + \tan ( v + 7 ) + \frac { n ^ { 4 } } { n + 1 } d u	integral	real_classroom_camscanner_original	42	long_41_55	750	107	train
S002-I04	\int _ { 2 } ^ { 9 } v \cdot n ^ { 2 } + n ^ { 3 } + \sqrt { k ^ { 2 } + 2 } + \gamma m + \frac { 4 a } { a + 5 } d v	integral	real_classroom_camscanner_original	49	long_41_55	750	107	train
S002-I05	\int _ { 3 } ^ { 5 } \tan ( x + 7 ) + \tan k + \gamma m + \frac { 4 a } { a + 5 } d x	integral	real_classroom_camscanner_original	34	normal_26_40	750	106	train
S002-I06	\int _ { 0 } ^ { 6 } y ^ { 3 } + \frac { m ^ { 4 } } { m + 1 } d y	integral	real_classroom_camscanner_original	30	normal_26_40	750	107	train
S002-I07	\int _ { 1 } ^ { 7 } \tan t + \sqrt { a ^ { 2 } + 2 } + b \cdot u ^ { 2 } d t	integral	real_classroom_camscanner_original	32	normal_26_40	750	107	train
S002-I08	\int _ { 2 } ^ { 8 } \frac { u ^ { 4 } } { u + 1 } + \gamma b d u	integral	real_classroom_camscanner_original	27	normal_26_40	750	106	train
S002-I09	\int _ { 3 } ^ { 9 } \sqrt { v ^ { 2 } + 2 } + \frac { 4 x } { x + 5 } d v	integral	real_classroom_camscanner_original	32	normal_26_40	750	107	train
S002-I10	\int _ { 0 } ^ { 5 } \gamma x + y \cdot u ^ { 2 } + \sin t + \frac { u ^ { 4 } } { u + 9 } d x	integral	real_classroom_camscanner_original	38	normal_26_40	750	108	train
S003-I01	\int _ { 1 } ^ { 6 } \frac { 4 y } { y + 5 } + \sin ( t + 6 ) d y	integral	real_classroom_camscanner_original	28	normal_26_40	766	107	train
S003-I02	\int _ { 2 } ^ { 7 } t \cdot u ^ { 2 } + u ^ { 6 } + \sqrt { v ^ { 2 } + 1 } d t	integral	real_classroom_camscanner_original	35	normal_26_40	766	108	train
S003-I03	\int _ { 3 } ^ { 8 } \sin ( u + 6 ) + \sin v + \theta n + \frac { 3 k } { k + 4 } d u	integral	real_classroom_camscanner_original	34	normal_26_40	766	108	train
S003-I04	\int _ { 0 } ^ { 9 } v ^ { 6 } + \frac { n ^ { 4 } } { n + 9 } d v	integral	real_classroom_camscanner_original	30	normal_26_40	766	109	train
S003-I05	\int _ { 1 } ^ { 5 } \sin x + \sqrt { k ^ { 2 } + 1 } + m \cdot y ^ { 2 } d x	integral	real_classroom_camscanner_original	32	normal_26_40	766	108	train
S003-I06	\int _ { 2 } ^ { 6 } \frac { y ^ { 4 } } { y + 9 } + \theta m d y	integral	real_classroom_camscanner_original	27	normal_26_40	766	109	train
S003-I07	\int _ { 3 } ^ { 7 } \sqrt { t ^ { 2 } + 1 } + \frac { 3 a } { a + 4 } + b ^ { 4 } + \ln x d t	integral	real_classroom_camscanner_original	41	long_41_55	766	108	train
S003-I08	\int _ { 0 } ^ { 8 } \theta u + b \cdot y ^ { 2 } + \ln x + \frac { y ^ { 4 } } { y + 8 } + \sqrt { t ^ { 2 } + 9 } d u	integral	real_classroom_camscanner_original	49	long_41_55	766	109	train
S003-I09	\int _ { 1 } ^ { 9 } \frac { 3 v } { v + 4 } + \ln ( x + 5 ) d v	integral	real_classroom_camscanner_original	28	normal_26_40	766	109	train
S003-I10	\int _ { 2 } ^ { 5 } x \cdot y ^ { 2 } + y ^ { 4 } + \sqrt { t ^ { 2 } + 9 } d x	integral	real_classroom_camscanner_original	35	normal_26_40	766	109	train
S004-I01	\int _ { 3 } ^ { 6 } \ln ( y + 5 ) + \ln t + \alpha u + \frac { 2 v } { v + 3 } d y	integral	real_classroom_camscanner_original	34	normal_26_40	758	106	train
S004-I02	\int _ { 0 } ^ { 7 } t ^ { 4 } + \frac { u ^ { 4 } } { u + 8 } d t	integral	real_classroom_camscanner_original	30	normal_26_40	758	107	train
S004-I03	\int _ { 1 } ^ { 8 } \ln u + \sqrt { v ^ { 2 } + 9 } + n \cdot b ^ { 2 } + \cos ( k + 4 ) + m ^ { 2 } d u	integral	real_classroom_camscanner_original	45	long_41_55	758	106	train
S004-I04	\int _ { 2 } ^ { 9 } \frac { v ^ { 4 } } { v + 8 } + \alpha n d v	integral	real_classroom_camscanner_original	27	normal_26_40	758	107	train
S004-I05	\int _ { 3 } ^ { 5 } \sqrt { x ^ { 2 } + 9 } + \frac { 2 k } { k + 3 } d x	integral	real_classroom_camscanner_original	32	normal_26_40	758	107	train
S004-I06	\int _ { 0 } ^ { 6 } \alpha y + m \cdot b ^ { 2 } + \cos a + \frac { b ^ { 4 } } { b + 7 } d y	integral	real_classroom_camscanner_original	38	normal_26_40	758	108	train
S004-I07	\int _ { 1 } ^ { 7 } \frac { 2 t } { t + 3 } + \cos ( a + 4 ) d t	integral	real_classroom_camscanner_original	28	normal_26_40	758	107	train
S004-I08	\int _ { 2 } ^ { 8 } u \cdot b ^ { 2 } + b ^ { 2 } + \sqrt { x ^ { 2 } + 8 } d u	integral	real_classroom_camscanner_original	35	normal_26_40	758	107	train
S004-I09	\int _ { 3 } ^ { 9 } \cos ( v + 4 ) + \cos x + \gamma y + \frac { 1 t } { t + 2 } d v	integral	real_classroom_camscanner_original	34	normal_26_40	758	108	train
S004-I10	\int _ { 0 } ^ { 5 } x ^ { 2 } + \frac { y ^ { 4 } } { y + 7 } d x	integral	real_classroom_camscanner_original	30	normal_26_40	758	108	train
S005-I01	\int _ { 1 } ^ { 6 } \cos y + \sqrt { t ^ { 2 } + 8 } + u \cdot m ^ { 2 } d y	integral	real_classroom_camscanner_original	32	normal_26_40	768	108	train
S005-I02	\int _ { 2 } ^ { 7 } \frac { t ^ { 4 } } { t + 7 } + \gamma u + \log ( v + 3 ) + n ^ { 5 } + \log k + \frac { m ^ { 4 } } { m + 6 } d t	integral	real_classroom_camscanner_original	57	stress_56_80	768	107	train
S005-I03	\int _ { 3 } ^ { 8 } \sqrt { u ^ { 2 } + 8 } + \frac { 1 v } { v + 2 } d u	integral	real_classroom_camscanner_original	32	normal_26_40	768	108	train
S005-I04	\int _ { 0 } ^ { 9 } \gamma v + n \cdot m ^ { 2 } + \log k + \frac { m ^ { 4 } } { m + 6 } d v	integral	real_classroom_camscanner_original	38	normal_26_40	768	108	train
S005-I05	\int _ { 1 } ^ { 5 } \frac { 1 x } { x + 2 } + \log ( k + 3 ) d x	integral	real_classroom_camscanner_original	28	normal_26_40	768	107	train
S005-I06	\int _ { 2 } ^ { 6 } y \cdot m ^ { 2 } + m ^ { 5 } + \sqrt { a ^ { 2 } + 7 } d y	integral	real_classroom_camscanner_original	35	normal_26_40	768	108	train
S005-I07	\int _ { 3 } ^ { 7 } \log ( t + 3 ) + \log a + \theta b + \frac { 9 x } { x + 1 } d t	integral	real_classroom_camscanner_original	34	normal_26_40	768	107	train
S005-I08	\int _ { 0 } ^ { 8 } u ^ { 5 } + \frac { b ^ { 4 } } { b + 6 } d u	integral	real_classroom_camscanner_original	30	normal_26_40	768	108	train
S005-I09	\int _ { 1 } ^ { 9 } \log v + \sqrt { x ^ { 2 } + 7 } + y \cdot n ^ { 2 } d v	integral	real_classroom_camscanner_original	32	normal_26_40	768	109	train
S005-I10	\int _ { 2 } ^ { 5 } \frac { x ^ { 4 } } { x + 6 } + \theta y + \tan ( t + 2 ) + u ^ { 3 } + \tan v d x	integral	real_classroom_camscanner_original	43	long_41_55	768	109	train
S006-I01	\int _ { 3 } ^ { 6 } \sqrt { y ^ { 2 } + 7 } + \frac { 9 t } { t + 1 } d y	integral	real_classroom_camscanner_original	32	normal_26_40	745	106	train
S006-I02	\int _ { 0 } ^ { 7 } \theta t + u \cdot n ^ { 2 } + \tan v + \frac { n ^ { 4 } } { n + 5 } d t	integral	real_classroom_camscanner_original	38	normal_26_40	745	107	train
S006-I03	\int _ { 1 } ^ { 8 } \frac { 9 u } { u + 1 } + \tan ( v + 2 ) d u	integral	real_classroom_camscanner_original	28	normal_26_40	745	106	train
S006-I04	\int _ { 2 } ^ { 9 } v \cdot n ^ { 2 } + n ^ { 3 } + \sqrt { k ^ { 2 } + 6 } d v	integral	real_classroom_camscanner_original	35	normal_26_40	745	108	train
S006-I05	\int _ { 3 } ^ { 5 } \tan ( x + 2 ) + \tan k + \alpha m + \frac { 8 a } { a + 9 } + b \cdot u ^ { 2 } + \sin ( x + 1 ) + y ^ { 6 } + \sin t d x	integral	real_classroom_camscanner_original	58	stress_56_80	745	106	train
S006-I06	\int _ { 0 } ^ { 6 } y ^ { 3 } + \frac { m ^ { 4 } } { m + 5 } + \frac { 8 a } { a + 9 } + b \cdot u ^ { 2 } + \sin ( x + 1 ) d y	integral	real_classroom_camscanner_original	56	stress_56_80	745	108	train
S006-I07	\int _ { 1 } ^ { 7 } \tan t + \sqrt { a ^ { 2 } + 6 } + b \cdot u ^ { 2 } + \sin ( x + 1 ) + y ^ { 6 } + \sin t + \frac { u ^ { 4 } } { u + 4 } d t	integral	real_classroom_camscanner_original	62	stress_56_80	745	106	train
S006-I08	\int _ { 2 } ^ { 8 } \frac { u ^ { 4 } } { u + 5 } + \alpha b d u	integral	real_classroom_camscanner_original	27	normal_26_40	745	108	train
S006-I09	\int _ { 3 } ^ { 9 } \sqrt { v ^ { 2 } + 6 } + \frac { 8 x } { x + 9 } d v	integral	real_classroom_camscanner_original	32	normal_26_40	745	108	train
S006-I10	\int _ { 0 } ^ { 5 } \alpha x + y \cdot u ^ { 2 } + \sin t + \frac { u ^ { 4 } } { u + 4 } d x	integral	real_classroom_camscanner_original	38	normal_26_40	745	109	train
S007-I01	\int _ { 1 } ^ { 6 } \frac { 8 y } { y + 9 } + \sin ( t + 1 ) d y	integral	real_classroom_camscanner_original	28	normal_26_40	761	107	train
S007-I02	\int _ { 2 } ^ { 7 } t \cdot u ^ { 2 } + u ^ { 6 } + \sqrt { v ^ { 2 } + 5 } d t	integral	real_classroom_camscanner_original	35	normal_26_40	761	108	train
S007-I03	\int _ { 3 } ^ { 8 } \sin ( u + 1 ) + \sin v + \gamma n + \frac { 7 k } { k + 8 } + m \cdot y ^ { 2 } d u	integral	real_classroom_camscanner_original	42	long_41_55	761	106	train
S007-I04	\int _ { 0 } ^ { 9 } v ^ { 6 } + \frac { n ^ { 4 } } { n + 4 } d v	integral	real_classroom_camscanner_original	30	normal_26_40	761	108	train
S007-I06	\int _ { 2 } ^ { 6 } \frac { y ^ { 4 } } { y + 4 } + \gamma m d y	integral	real_classroom_camscanner_original	27	normal_26_40	761	108	train
S007-I07	\int _ { 3 } ^ { 7 } \sqrt { t ^ { 2 } + 5 } + \frac { 7 a } { a + 8 } d t	integral	real_classroom_camscanner_original	32	normal_26_40	761	107	train
S007-I09	\int _ { 1 } ^ { 9 } \frac { 7 v } { v + 8 } + \ln ( x + 9 ) d v	integral	real_classroom_camscanner_original	28	normal_26_40	761	108	train
S007-I10	\int _ { 2 } ^ { 5 } x \cdot y ^ { 2 } + y ^ { 4 } + \sqrt { t ^ { 2 } + 4 } d x	integral	real_classroom_camscanner_original	35	normal_26_40	761	109	train
S008-I01	\int _ { 3 } ^ { 6 } \ln ( y + 9 ) + \ln t + \theta u + \frac { 6 v } { v + 7 } + n \cdot b ^ { 2 } d y	integral	real_classroom_camscanner_original	42	long_41_55	757	107	train
S008-I02	\int _ { 0 } ^ { 7 } t ^ { 4 } + \frac { u ^ { 4 } } { u + 3 } d t	integral	real_classroom_camscanner_original	30	normal_26_40	757	107	train
S008-I03	\int _ { 1 } ^ { 8 } \ln u + \sqrt { v ^ { 2 } + 4 } + n \cdot b ^ { 2 } d u	integral	real_classroom_camscanner_original	32	normal_26_40	757	107	train
S008-I04	\int _ { 2 } ^ { 9 } \frac { v ^ { 4 } } { v + 3 } + \theta n d v	integral	real_classroom_camscanner_original	27	normal_26_40	757	108	train
S008-I05	\int _ { 3 } ^ { 5 } \sqrt { x ^ { 2 } + 4 } + \frac { 6 k } { k + 7 } d x	integral	real_classroom_camscanner_original	32	normal_26_40	757	108	train
S008-I06	\int _ { 0 } ^ { 6 } \theta y + m \cdot b ^ { 2 } + \cos a + \frac { b ^ { 4 } } { b + 2 } d y	integral	real_classroom_camscanner_original	38	normal_26_40	757	108	train
S008-I07	\int _ { 1 } ^ { 7 } \frac { 6 t } { t + 7 } + \cos ( a + 8 ) + \frac { b ^ { 4 } } { b + 2 } + \sqrt { x ^ { 2 } + 3 } + \alpha y d t	integral	real_classroom_camscanner_original	56	stress_56_80	757	107	train
S008-I08	\int _ { 2 } ^ { 8 } u \cdot b ^ { 2 } + b ^ { 2 } + \sqrt { x ^ { 2 } + 3 } + \alpha y + \frac { 5 t } { t + 6 } d u	integral	real_classroom_camscanner_original	49	long_41_55	757	109	train
S008-I09	\int _ { 3 } ^ { 9 } \cos ( v + 8 ) + \cos x + \alpha y + \frac { 5 t } { t + 6 } d v	integral	real_classroom_camscanner_original	34	normal_26_40	757	108	train
S008-I10	\int _ { 0 } ^ { 5 } x ^ { 2 } + \frac { y ^ { 4 } } { y + 2 } d x	integral	real_classroom_camscanner_original	30	normal_26_40	757	108	train
S009-I01	\int _ { 1 } ^ { 6 } \cos y + \sqrt { t ^ { 2 } + 3 } + u \cdot m ^ { 2 } d y	integral	real_classroom_camscanner_original	32	normal_26_40	734	107	train
S009-I02	\int _ { 2 } ^ { 7 } \frac { t ^ { 4 } } { t + 2 } + \alpha u d t	integral	real_classroom_camscanner_original	27	normal_26_40	734	107	train
S009-I03	\int _ { 3 } ^ { 8 } \sqrt { u ^ { 2 } + 3 } + \frac { 5 v } { v + 6 } d u	integral	real_classroom_camscanner_original	32	normal_26_40	734	107	train
S009-I04	\int _ { 0 } ^ { 9 } \alpha v + n \cdot m ^ { 2 } + \log k + \frac { m ^ { 4 } } { m + 1 } d v	integral	real_classroom_camscanner_original	38	normal_26_40	734	107	train
S009-I05	\int _ { 1 } ^ { 5 } \frac { 5 x } { x + 6 } + \log ( k + 7 ) d x	integral	real_classroom_camscanner_original	28	normal_26_40	734	108	train
S009-I06	\int _ { 2 } ^ { 6 } y \cdot m ^ { 2 } + m ^ { 5 } + \sqrt { a ^ { 2 } + 2 } + \gamma b + \frac { 4 x } { x + 5 } + y \cdot n ^ { 2 } d y	integral	real_classroom_camscanner_original	57	stress_56_80	734	108	train
S009-I07	\int _ { 3 } ^ { 7 } \log ( t + 7 ) + \log a + \gamma b + \frac { 4 x } { x + 5 } + y \cdot n ^ { 2 } d t	integral	real_classroom_camscanner_original	42	long_41_55	734	107	train
S009-I08	\int _ { 0 } ^ { 8 } u ^ { 5 } + \frac { b ^ { 4 } } { b + 1 } + \frac { 4 x } { x + 5 } + y \cdot n ^ { 2 } + \tan ( t + 6 ) d u	integral	real_classroom_camscanner_original	56	stress_56_80	734	108	train
S009-I09	\int _ { 1 } ^ { 9 } \log v + \sqrt { x ^ { 2 } + 2 } + y \cdot n ^ { 2 } d v	integral	real_classroom_camscanner_original	32	normal_26_40	734	108	train
S009-I10	\int _ { 2 } ^ { 5 } \frac { x ^ { 4 } } { x + 1 } + \gamma y d x	integral	real_classroom_camscanner_original	27	normal_26_40	734	108	train
S010-I01	\int _ { 3 } ^ { 6 } \sqrt { y ^ { 2 } + 2 } + \frac { 4 t } { t + 5 } + u ^ { 3 } + \tan v d y	integral	real_classroom_camscanner_original	41	long_41_55	749	108	train
S010-I02	\int _ { 0 } ^ { 7 } \gamma t + u \cdot n ^ { 2 } + \tan v + \frac { n ^ { 4 } } { n + 9 } d t	integral	real_classroom_camscanner_original	38	normal_26_40	749	107	train
S010-I03	\int _ { 1 } ^ { 8 } \frac { 4 u } { u + 5 } + \tan ( v + 6 ) + \frac { n ^ { 4 } } { n + 9 } d u	integral	real_classroom_camscanner_original	42	long_41_55	749	106	train
S010-I04	\int _ { 2 } ^ { 9 } v \cdot n ^ { 2 } + n ^ { 3 } + \sqrt { k ^ { 2 } + 1 } + \theta m + \frac { 3 a } { a + 4 } d v	integral	real_classroom_camscanner_original	49	long_41_55	749	108	train
S010-I05	\int _ { 3 } ^ { 5 } \tan ( x + 6 ) + \tan k + \theta m + \frac { 3 a } { a + 4 } d x	integral	real_classroom_camscanner_original	34	normal_26_40	749	106	train
S010-I06	\int _ { 0 } ^ { 6 } y ^ { 3 } + \frac { m ^ { 4 } } { m + 9 } + \frac { 3 a } { a + 4 } + b \cdot u ^ { 2 } + \sin ( x + 5 ) d y	integral	real_classroom_camscanner_original	56	stress_56_80	749	108	train
S010-I07	\int _ { 1 } ^ { 7 } \tan t + \sqrt { a ^ { 2 } + 1 } + b \cdot u ^ { 2 } d t	integral	real_classroom_camscanner_original	32	normal_26_40	749	108	train
S010-I08	\int _ { 2 } ^ { 8 } \frac { u ^ { 4 } } { u + 9 } + \theta b d u	integral	real_classroom_camscanner_original	27	normal_26_40	749	107	train
S010-I09	\int _ { 3 } ^ { 9 } \sqrt { v ^ { 2 } + 1 } + \frac { 3 x } { x + 4 } + y ^ { 6 } + \sin t + \frac { u ^ { 4 } } { u + 8 } + \sqrt { v ^ { 2 } + 9 } d v	integral	real_classroom_camscanner_original	66	stress_56_80	749	108	train
S010-I10	\int _ { 0 } ^ { 5 } \theta x + y \cdot u ^ { 2 } + \sin t + \frac { u ^ { 4 } } { u + 8 } + \sqrt { v ^ { 2 } + 9 } + \alpha n + \frac { 2 k } { k + 3 } d x	integral	real_classroom_camscanner_original	63	stress_56_80	749	108	train
S011-I01	\int _ { 1 } ^ { 6 } \frac { 3 y } { y + 4 } + \sin ( t + 5 ) + \frac { u ^ { 4 } } { u + 8 } + \sqrt { v ^ { 2 } + 9 } + \alpha n d y	integral	real_classroom_camscanner_original	56	stress_56_80	742	107	train
S011-I02	\int _ { 2 } ^ { 7 } t \cdot u ^ { 2 } + u ^ { 6 } + \sqrt { v ^ { 2 } + 9 } + \alpha n + \frac { 2 k } { k + 3 } d t	integral	real_classroom_camscanner_original	49	long_41_55	742	108	train
S011-I03	\int _ { 3 } ^ { 8 } \sin ( u + 5 ) + \sin v + \alpha n + \frac { 2 k } { k + 3 } d u	integral	real_classroom_camscanner_original	34	normal_26_40	742	107	train

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University HMER RealClassroom

University HMER RealClassroom is a curated dataset of 1,636 handwritten university-calculus expressions captured under practical classroom-style conditions. Each image is paired with a manually reviewed tokenized LaTeX transcription and structured metadata describing expression family and sequence-length difficulty.

This initial Hub release is private while ownership, privacy, annotation quality, and licensing are reviewed. The current license: other marker must be replaced by an explicit license before any public release.

Dataset summary

Split	Samples	Intended use
`train`	1,103	Real-domain fine-tuning
`validation`	259	Checkpoint selection and validation analysis
`test`	274	Frozen blind evaluation
Total	1,636

The split membership is frozen. The test split was not used for checkpoint selection.

Data fields

Field	Type	Description
`image`	image	Cropped handwritten mathematical expression
`sample_id`	string	Stable anonymized sample identifier
`latex`	string	Space-tokenized LaTeX ground truth
`category`	string	Expression family
`source`	string	Capture/processing source descriptor
`token_count`	integer	Number of ground-truth tokens
`severity`	string	Token-length difficulty band
`width`	integer	Original image width
`height`	integer	Original image height
`split`	string	`train`, `validation`, or `test`

The repository uses Hugging Face ImageFolder layout. In each split, metadata.csv maps file_name to the remaining fields.

Category distribution

Category	Train	Validation	Test
`integral`	407	0	0
`derivative_partial`	245	0	0
`limit`	178	0	0
`sum_series`	255	0	0
`log_exp`	18	125	0
`mixed_nested`	0	134	274

The validation split deliberately contains more logarithmic, natural-logarithm, and nested-exponential expressions. The frozen test split contains only mixed_nested expressions and no dedicated e^nested category. Consequently, validation and test scores should not be interpreted as if both splits were identically distributed.

Difficulty distribution

Severity	Train	Validation	Test	Total
`normal_26_40`	801	202	208	1,211
`long_41_55`	218	40	48	306
`stress_56_80`	84	17	18	119

Benchmark context

Representative recorded results:

Model	Validation ExpRate	Validation TER	Test ExpRate	Test TER
TAMER Original	1.93%	30.88%	4.38%	22.34%
TAMER A0 RealFT	53.28%	5.80%	69.34%	3.05%
TAMER A3 RealFT	56.37%	5.45%	71.17%	2.92%
Uni-MuMER zero-shot	14.67%	13.50%	23.72%	7.18%
Uni-MuMER LoRA	64.48%	4.62%	74.82%	3.38%

Metrics must be reproduced with the project's normalization and token-level evaluation pipeline. ExpRate is exact expression recognition rate; TER is token error rate.

Collection and processing

Expressions were written and captured to represent practical university-calculus HMER conditions. The published images are already cropped to expression regions. Dataset preparation verifies:

every manifest entry resolves to an image;
all images decode successfully;
sample IDs and image hashes are unique across splits;
copied images match source SHA-256 values;
no image contains EXIF metadata;
metadata contains no absolute local paths.

audit_report.json records split-level counts and distributions. image_checksums.sha256 records checksums for all 1,636 published images.

Intended uses

handwritten mathematical expression recognition;
image-to-LaTeX transcription;
real-domain adaptation;
comparison of specialist HMER models and multimodal vision-language models;
robustness and error analysis for university-calculus notation.

Limitations and biases

The dataset is relatively small.
The writer/capture diversity is limited and should not be assumed to represent all universities, devices, handwriting styles, or lighting conditions.
Split distributions differ by design.
The vocabulary originates from the associated TAMER/HME pipeline and does not cover all notation used across Calculus I–III.
Exact-match performance can penalize semantically equivalent LaTeX strings.
Dataset acceptance does not imply that every expression is equally difficult for humans or models.

Operator-bound layout bias

The dataset has limited spatial diversity in the placement of integral and summation bounds. In many observed samples, upper and lower bounds are written diagonally or to the right of the \int or \sum operator rather than being clearly stacked above and below it. This is a valid and common handwriting convention, but canonical display-style layouts with vertically aligned bounds are underrepresented.

Consequently, models trained or adapted on this dataset may overfit to right-offset operator bounds and generalize less effectively to other two-dimensional layouts. Possible failure modes include confusing a bound with a superscript or subscript of a neighboring symbol. Results on the blind-test split should therefore not be interpreted as a complete measurement of robustness to operator-bound placement, especially when the training and evaluation samples share similar handwriting conventions.

Future dataset versions should include vertically stacked, diagonally offset, compact inline, and widely spaced bounds from a broader range of writers. Controlled operator-bound augmentation and layout-specific evaluation metrics are also recommended. This limitation is currently qualitative; the frequency of each layout type has not yet been formally annotated or quantified.

Privacy and release status

The preparation audit found no EXIF metadata and uses anonymized sample IDs. Before a public release, the maintainer must still visually review all images, confirm the right to redistribute every sample, choose an explicit license, and document any consent process. Until then, this repository should remain private.

Citation

A formal citation will be added when the associated final-project report or paper is published.

Maintainer

Dataset repository owner: tuan3110.

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