test gauleg.adb on interval -1.0 to 1.0  ordinates, weights
x( 1)= 0.00000000000000E+00w( 1)= 2.00000000000000E+00
              integral(1.0, -1.0..1.0)= 2.00000000000000E+00

x( 1)=-5.77350269189626E-01w( 1)= 1.00000000000000E+00
x( 2)= 5.77350269189626E-01w( 2)= 1.00000000000000E+00
              integral(1.0, -1.0..1.0)= 2.00000000000000E+00

x( 1)=-7.74596669241483E-01w( 1)= 5.55555555555552E-01
x( 2)= 0.00000000000000E+00w( 2)= 8.88888888888889E-01
x( 3)= 7.74596669241483E-01w( 3)= 5.55555555555552E-01
              integral(1.0, -1.0..1.0)= 1.99999999999999E+00

x( 1)=-8.61136311594053E-01w( 1)= 3.47854845137448E-01
x( 2)=-3.39981043584856E-01w( 2)= 6.52145154862546E-01
x( 3)= 3.39981043584856E-01w( 3)= 6.52145154862546E-01
x( 4)= 8.61136311594053E-01w( 4)= 3.47854845137448E-01
              integral(1.0, -1.0..1.0)= 1.99999999999999E+00

x( 1)=-9.06179845938664E-01w( 1)= 2.36926885056182E-01
x( 2)=-5.38469310105683E-01w( 2)= 4.78628670499366E-01
x( 3)= 0.00000000000000E+00w( 3)= 5.68888888888889E-01
x( 4)= 5.38469310105683E-01w( 4)= 4.78628670499366E-01
x( 5)= 9.06179845938664E-01w( 5)= 2.36926885056182E-01
              integral(1.0, -1.0..1.0)= 1.99999999999999E+00

x( 1)=-9.32469514203152E-01w( 1)= 1.71324492379163E-01
x( 2)=-6.61209386466264E-01w( 2)= 3.60761573048139E-01
x( 3)=-2.38619186083197E-01w( 3)= 4.67913934572689E-01
x( 4)= 2.38619186083197E-01w( 4)= 4.67913934572689E-01
x( 5)= 6.61209386466264E-01w( 5)= 3.60761573048139E-01
x( 6)= 9.32469514203152E-01w( 6)= 1.71324492379163E-01
              integral(1.0, -1.0..1.0)= 1.99999999999998E+00

x( 1)=-9.49107912342758E-01w( 1)= 1.29484966168863E-01
x( 2)=-7.41531185599394E-01w( 2)= 2.79705391489277E-01
x( 3)=-4.05845151377397E-01w( 3)= 3.81830050505119E-01
x( 4)= 0.00000000000000E+00w( 4)= 4.17959183673469E-01
x( 5)= 4.05845151377397E-01w( 5)= 3.81830050505119E-01
x( 6)= 7.41531185599394E-01w( 6)= 2.79705391489277E-01
x( 7)= 9.49107912342758E-01w( 7)= 1.29484966168863E-01
              integral(1.0, -1.0..1.0)= 1.99999999999999E+00

x( 1)=-9.60289856497536E-01w( 1)= 1.01228536290371E-01
x( 2)=-7.96666477413627E-01w( 2)= 2.22381034453374E-01
x( 3)=-5.25532409916329E-01w( 3)= 3.13706645877887E-01
x( 4)=-1.83434642495650E-01w( 4)= 3.62683783378362E-01
x( 5)= 1.83434642495650E-01w( 5)= 3.62683783378362E-01
x( 6)= 5.25532409916329E-01w( 6)= 3.13706645877887E-01
x( 7)= 7.96666477413627E-01w( 7)= 2.22381034453374E-01
x( 8)= 9.60289856497536E-01w( 8)= 1.01228536290371E-01
              integral(1.0, -1.0..1.0)= 1.99999999999999E+00

x( 1)=-9.68160239507626E-01w( 1)= 8.12743883615689E-02
x( 2)=-8.36031107326636E-01w( 2)= 1.80648160694857E-01
x( 3)=-6.13371432700590E-01w( 3)= 2.60610696402935E-01
x( 4)=-3.24253423403809E-01w( 4)= 3.12347077040002E-01
x( 5)= 0.00000000000000E+00w( 5)= 3.30239355001260E-01
x( 6)= 3.24253423403809E-01w( 6)= 3.12347077040002E-01
x( 7)= 6.13371432700590E-01w( 7)= 2.60610696402935E-01
x( 8)= 8.36031107326636E-01w( 8)= 1.80648160694857E-01
x( 9)= 9.68160239507626E-01w( 9)= 8.12743883615689E-02
              integral(1.0, -1.0..1.0)= 1.99999999999999E+00

x( 1)=-9.73906528517172E-01w( 1)= 6.66713443086836E-02
x( 2)=-8.65063366688985E-01w( 2)= 1.49451349150580E-01
x( 3)=-6.79409568299024E-01w( 3)= 2.19086362515982E-01
x( 4)=-4.33395394129247E-01w( 4)= 2.69266719309992E-01
x( 5)=-1.48874338981631E-01w( 5)= 2.95524224714753E-01
x( 6)= 1.48874338981631E-01w( 6)= 2.95524224714753E-01
x( 7)= 4.33395394129247E-01w( 7)= 2.69266719309992E-01
x( 8)= 6.79409568299024E-01w( 8)= 2.19086362515982E-01
x( 9)= 8.65063366688985E-01w( 9)= 1.49451349150580E-01
x( 10)= 9.73906528517172E-01w( 10)= 6.66713443086836E-02
              integral(1.0, -1.0..1.0)= 1.99999999999998E+00

x( 1)=-9.78228658146057E-01w( 1)= 5.56685671161692E-02
x( 2)=-8.87062599768095E-01w( 2)= 1.25580369464905E-01
x( 3)=-7.30152005574049E-01w( 3)= 1.86290210927734E-01
x( 4)=-5.19096129206812E-01w( 4)= 2.33193764591978E-01
x( 5)=-2.69543155952345E-01w( 5)= 2.62804544510247E-01
x( 6)= 0.00000000000000E+00w( 6)= 2.72925086777901E-01
x( 7)= 2.69543155952345E-01w( 7)= 2.62804544510247E-01
x( 8)= 5.19096129206812E-01w( 8)= 2.33193764591978E-01
x( 9)= 7.30152005574049E-01w( 9)= 1.86290210927734E-01
x( 10)= 8.87062599768095E-01w( 10)= 1.25580369464905E-01
x( 11)= 9.78228658146057E-01w( 11)= 5.56685671161692E-02
              integral(1.0, -1.0..1.0)= 1.99999999999997E+00

x( 1)=-9.81560634246719E-01w( 1)= 4.71753363865084E-02
x( 2)=-9.04117256370475E-01w( 2)= 1.06939325995318E-01
x( 3)=-7.69902674194305E-01w( 3)= 1.60078328543346E-01
x( 4)=-5.87317954286617E-01w( 4)= 2.03167426723066E-01
x( 5)=-3.67831498998180E-01w( 5)= 2.33492536538355E-01
x( 6)=-1.25233408511469E-01w( 6)= 2.49147045813403E-01
x( 7)= 1.25233408511469E-01w( 7)= 2.49147045813403E-01
x( 8)= 3.67831498998180E-01w( 8)= 2.33492536538355E-01
x( 9)= 5.87317954286617E-01w( 9)= 2.03167426723066E-01
x( 10)= 7.69902674194305E-01w( 10)= 1.60078328543346E-01
x( 11)= 9.04117256370475E-01w( 11)= 1.06939325995318E-01
x( 12)= 9.81560634246719E-01w( 12)= 4.71753363865084E-02
              integral(1.0, -1.0..1.0)= 1.99999999999999E+00

x( 1)=-9.84183054718588E-01w( 1)= 4.04840047653124E-02
x( 2)=-9.17598399222978E-01w( 2)= 9.21214998377285E-02
x( 3)=-8.01578090733310E-01w( 3)= 1.38873510219787E-01
x( 4)=-6.42349339440340E-01w( 4)= 1.78145980761946E-01
x( 5)=-4.48492751036447E-01w( 5)= 2.07816047536888E-01
x( 6)=-2.30458315955135E-01w( 6)= 2.26283180262897E-01
x( 7)= 0.00000000000000E+00w( 7)= 2.32551553230874E-01
x( 8)= 2.30458315955135E-01w( 8)= 2.26283180262897E-01
x( 9)= 4.48492751036447E-01w( 9)= 2.07816047536888E-01
x( 10)= 6.42349339440340E-01w( 10)= 1.78145980761946E-01
x( 11)= 8.01578090733310E-01w( 11)= 1.38873510219787E-01
x( 12)= 9.17598399222978E-01w( 12)= 9.21214998377285E-02
x( 13)= 9.84183054718588E-01w( 13)= 4.04840047653124E-02
              integral(1.0, -1.0..1.0)= 1.99999999999999E+00

x( 1)=-9.86283808696812E-01w( 1)= 3.51194603317485E-02
x( 2)=-9.28434883663574E-01w( 2)= 8.01580871597602E-02
x( 3)=-8.27201315069765E-01w( 3)= 1.21518570687903E-01
x( 4)=-6.87292904811685E-01w( 4)= 1.57203167158194E-01
x( 5)=-5.15248636358154E-01w( 5)= 1.85538397477936E-01
x( 6)=-3.19112368927890E-01w( 6)= 2.05198463721295E-01
x( 7)=-1.08054948707344E-01w( 7)= 2.15263853463158E-01
x( 8)= 1.08054948707344E-01w( 8)= 2.15263853463158E-01
x( 9)= 3.19112368927890E-01w( 9)= 2.05198463721295E-01
x( 10)= 5.15248636358154E-01w( 10)= 1.85538397477936E-01
x( 11)= 6.87292904811685E-01w( 11)= 1.57203167158194E-01
x( 12)= 8.27201315069765E-01w( 12)= 1.21518570687903E-01
x( 13)= 9.28434883663574E-01w( 13)= 8.01580871597602E-02
x( 14)= 9.86283808696812E-01w( 14)= 3.51194603317485E-02
              integral(1.0, -1.0..1.0)= 1.99999999999999E+00

x( 1)=-9.87992518020485E-01w( 1)= 3.07532419961146E-02
x( 2)=-9.37273392400706E-01w( 2)= 7.03660474881081E-02
x( 3)=-8.48206583410427E-01w( 3)= 1.07159220467172E-01
x( 4)=-7.24417731360170E-01w( 4)= 1.39570677926154E-01
x( 5)=-5.70972172608539E-01w( 5)= 1.66269205816992E-01
x( 6)=-3.94151347077563E-01w( 6)= 1.86161000015562E-01
x( 7)=-2.01194093997435E-01w( 7)= 1.98431485327111E-01
x( 8)= 0.00000000000000E+00w( 8)= 2.02578241925561E-01
x( 9)= 2.01194093997435E-01w( 9)= 1.98431485327111E-01
x( 10)= 3.94151347077563E-01w( 10)= 1.86161000015562E-01
x( 11)= 5.70972172608539E-01w( 11)= 1.66269205816992E-01
x( 12)= 7.24417731360170E-01w( 12)= 1.39570677926154E-01
x( 13)= 8.48206583410427E-01w( 13)= 1.07159220467172E-01
x( 14)= 9.37273392400706E-01w( 14)= 7.03660474881081E-02
x( 15)= 9.87992518020485E-01w( 15)= 3.07532419961146E-02
              integral(1.0, -1.0..1.0)= 1.99999999999999E+00

integral (0.5,1.0) sin(x) dx =  3.37275337402820E-01
integral (0.5,1.0) sin(x) dx =  3.37280258658711E-01
integral (0.5,1.0) sin(x) dx =  3.37280256021483E-01
integral (0.5,1.0) sin(x) dx =  3.37280256022231E-01
integral (0.5,1.0) sin(x) dx =  3.37280256022230E-01
integral (0.5,1.0) sin(x) dx =  3.37280256022231E-01
integral (0.5,1.0) sin(x) dx =  3.37280256022231E-01
integral (0.5,1.0) sin(x) dx =  3.37280256022231E-01
integral (0.5,1.0) sin(x) dx =  3.37280256022230E-01
-cos(1.0)+cos(0.5) =  3.37280256022233E-01
Maple says 3.372802560E-01

integral (0.5,5.0) exp(x) dx =  1.38621353525362E+02
integral (0.5,5.0) exp(x) dx =  1.46426441517713E+02
integral (0.5,5.0) exp(x) dx =  1.46756900639624E+02
integral (0.5,5.0) exp(x) dx =  1.46764332896365E+02
integral (0.5,5.0) exp(x) dx =  1.46764436833358E+02
integral (0.5,5.0) exp(x) dx =  1.46764437824972E+02
integral (0.5,5.0) exp(x) dx =  1.46764437831838E+02
integral (0.5,5.0) exp(x) dx =  1.46764437831875E+02
integral (0.5,5.0) exp(x) dx =  1.46764437831875E+02
exp(5.0)-exp(0.5) =  1.46764437831876E+02
Maple says 1.467644378E+02

integral (0.5,5.0) mess(x) dx =  3.13565070117054E+11
integral (0.5,5.0) mess(x) dx =  3.33875441481890E+14
integral (0.5,5.0) mess(x) dx =  8.29976580337804E+15
integral (0.5,5.0) mess(x) dx =  4.20268820138059E+16
integral (0.5,5.0) mess(x) dx =  1.00860131815890E+17
integral (0.5,5.0) mess(x) dx =  1.64709518288183E+17
integral (0.5,5.0) mess(x) dx =  2.17390643607277E+17
integral (0.5,5.0) mess(x) dx =  2.53750719708527E+17
integral (0.5,5.0) mess(x) dx =  2.75736214225415E+17
integral (0.5,5.0) mess(x) dx =  2.87665034143839E+17
integral (0.5,5.0) mess(x) dx =  2.93554910945554E+17
integral (0.5,5.0) mess(x) dx =  2.96226282472341E+17
integral (0.5,5.0) mess(x) dx =  2.97346996889225E+17
integral (0.5,5.0) mess(x) dx =  2.97784295593249E+17
integral (0.5,5.0) mess(x) dx =  2.97943724837074E+17
integral (0.5,5.0) mess(x) dx =  2.97998245704574E+17
integral (0.5,5.0) mess(x) dx =  2.98015794531122E+17
integral (0.5,5.0) mess(x) dx =  2.98021127189695E+17
integral (0.5,5.0) mess(x) dx =  2.98022661227586E+17
integral (0.5,5.0) mess(x) dx =  2.98023080021824E+17
integral (0.5,5.0) mess(x) dx =  2.98023188769470E+17
integral (0.5,5.0) mess(x) dx =  2.98023215684549E+17
integral (0.5,5.0) mess(x) dx =  2.98023222046051E+17
integral (0.5,5.0) mess(x) dx =  2.98023223484466E+17
integral (0.5,5.0) mess(x) dx =  2.98023223796129E+17
integral (0.5,5.0) mess(x) dx =  2.98023223860942E+17
integral (0.5,5.0) mess(x) dx =  2.98023223873886E+17
integral (0.5,5.0) mess(x) dx =  2.98023223876378E+17
integral (0.5,5.0) mess(x) dx =  2.98023223876840E+17
((5.0**5.0)**5.0)-(0.5**0.5)**0.5 =  2.98023223876953E+17
Maple says 2.980232239E+17

Done.