> restart:
> Digits:=25:
> f:=3*sin(4*R+1)-1;
> _EnvAllSolutions := true;
> sol:=solve(f=0,R);
> 

                       f := 3 sin(4 R + 1) - 1


                       _EnvAllSolutions := true


                                                          Pi _Z1~
  sol := - 1/4 + 1/4 arcsin(1/3) - 1/2 arcsin(1/3) _B1~ + -------
                                                             2

           Pi _B1~
         + -------
              4

> plot(f,R=-4..4);

> evalf(subs(_Z1=2,_B1=0,sol));

                      2.976551880953323722736741

> tot:=0.0:
> for i from -10 to 10 do
>   x1:=subs(_Z1=i,_B1=1,sol);
>   x2:=subs(_Z1=i+1,_B1=0,sol);
>   dtot:=evalf(Int(1/sqrt(2*Pi)*exp(-x^2/2),x=x1..x2));
>   tot:=tot+dtot;
>   print(evalf([x1,x2,dtot,tot]));
> od:
> 

  [-15.25752433191504836697165, -14.30220771379053908880779,

                                      -46
        0.1370998221761861388305234 10   ,

                                      -46
        0.1370998221761861388305234 10   ]


  [-13.68672800512015174774033, -12.73141138699564246957647,

                                      -36
        0.1978071427272599425821954 10   ,

                                      -36
        0.1978071427409699247998140 10   ]


  [-12.11593167832525512850901, -11.16061506020074585034515,

                                       -27
        -0.3659532343933870272711977 10   ,

                                       -27
        -0.3659532341955798845302278 10   ]


  [-10.54513535153035850927769, -9.589818733405849231113831,

                                      -21
        0.4411726546546998002091494 10   ,

                                      -21
        0.4411722887014656046292649 10   ]


  [-8.974339024735461890046366, -8.019022406610952611882510,

                                      -15
        0.5328077898318555265027963 10   ,

                                      -15
        0.5328082310041442279684009 10   ]


  [-7.403542697940565270815045, -6.448226079816055992651188,

                                      -10
        0.5651713545674776276016157 10   ,

                                      -10
        0.5651766826497876690438954 10   ]


  [-5.832746371145668651583723, -4.877429753021159373419866,

                                      -6
        0.5346594042256590664900493 10  ,

                                      -6
        0.5347159218939240452569537 10  ]


  [-4.261950044350772032352402, -3.306633426226262754188545,

        0.0004619893108736211495048850,

        0.0004625240267955150735501420]


  [-2.691153717555875413121080, -1.735837099431366134957224,

        0.03773605225644048865378336, 0.03819857628323600372733350]


  [-1.120357390760978793889759, -0.1650407726364695157259019,

        0.3031751977350296323154051, 0.3413737740182656360427386]


  [0.4504389360339178253415627, 1.405755554158427103505420,

        0.2462986255740913632778515, 0.5876723995923569993205901]


  [2.021235262828814444572884, 2.976551880953323722736741,

        0.02017015972270004654292032, 0.6078425593150570458635104]


  [3.592031589623711063804206, 4.547348207748220341968062,

        0.0001613387284136850832865780, 0.6080038980434707309467970]


  [5.162827916418607683035527, 6.118144534543116961199384,

                                      -6
        0.1211500141930226496942031 10  , 0.6080040191934849239694467

        ]


  [6.733624243213504302266849, 7.688940861338013580430706,

                                      -11
        0.8266993193675119333476345 10   ,

        0.6080040192017519171631218]


  [8.304420570008400921498170, 9.259737188132910199662027,

                                      -16
        0.5014362553791884083951006 10   ,

        0.6080040192017519673067473]


  [9.875216896803297540729492, 10.83053351492780681889335,

                                      -22
        0.2665747435462588008613368 10   ,

        0.6080040192017519673067740]


  [11.44601322359819415996081, 12.40132984172270343812467,

                                       -27
        -0.3788272595184980027034315 10   ,

        0.6080040192017519673067740]


  [13.01680955039309077919213, 13.97212616851760005735599,

                                      -38
        0.4909341406938971689575118 10   ,

        0.6080040192017519673067740]


  [14.58760587718798739842345, 15.54292249531249667658732,

                                      -48
        0.2091203075901376708943104 10   ,

        0.6080040192017519673067740]


  [16.15840220398288401765478, 17.11371882210739329581864,

                                      -58
        0.4954843638488353530861810 10   ,

        0.6080040192017519673067740]

> 
