PRIMARY OBJECTIVES:
      I. To identify the maximum tolerated dose (MTD)/recommended phase 2 dose (RP2D) for a regimen
      combining WEE1 inhibitor AZD1775 (AZD1775) with belinostat in patients with
      refractory/relapsed acute myeloid leukemia (AML), chronic myeloid leukemia in blast crisis
      (CML-BC), or intermediate-2 or high-risk myelodysplastic syndrome (MDS), and selected
      previously untreated poor-prognosis patients with AML.
      SECONDARY OBJECTIVES:
      I. To describe the toxicities of this regimen. II. To observe and record anti-tumor activity.
      III. If responses are observed, to determine what relationship, if any, exists between such
      responses and tumor protein 53 (p53)/fms-related tyrosine kinase 3 (FLT3) mutational status.
      IV. To describe pharmacokinetic (PK) interactions, if any, between AZD1775 and belinostat.
      V. To test the feasibility of performing correlative studies involving leukemic blasts
      obtained pre-treatment and 24-hours post-treatment to determine if events associated with in
      vitro synergism (eg, down-regulation of phosphorylated [p]-Wee1 and p-checkpoint kinase 1
      [Chk1]; dephosphorylation of cyclin-dependent kinase-like 1 [cdc2] at both tyrosine [Tyr]15
      and threonine [Thr]14; increased expression of gamma H2A histone family, member X [H2A.X] and
      of p-histone H3 [HH3]) can be recapitulated following exposure to AZD1775 and belinostat in
      patients.
      OUTLINE: This is a dose-escalation study.
      Patients receive belinostat intravenously (IV) over 30-90 minutes once daily (QD) on days 1-5
      and 8-12 and WEE1 inhibitor AZD1775 orally (PO) QD on days 1-5 and 8-12. Courses repeat every
      21 days in the absence of disease progression or unacceptable toxicity. Patients achieving
      complete remission (CR), complete remission with incomplete blood count recovery (CRi),
      cytogenetic complete remission (CRc), or molecular complete remission (CRm) who do not go on
      to have stem cell transplant may only continue treatment for 3-4 additional courses after
      response.
      After completion of study treatment, all patients are followed up for 30 days and responding
      patients are followed up every 2 months for 1 year.
    
        Inclusion Criteria:
          -  Patients must have one of the following, histologically or cytologically confirmed:
               -  Acute myeloid leukemia (AML) [non- acute promyelocytic leukemia (APL) AML]
                    -  If previously treated:
                         -  AML that is relapsed or refractory to at least one prior line of
                            therapy
                    -  If previously untreated, must meet all of the following:
                         -  >= 60 years of age
                         -  Secondary or therapy-related AML
                         -  Does NOT bear favorable cytogenetic and/or molecular features, eg,
                            core-binding factor abnormalities, FLT3 Internal Tandem Duplication
                            (FLT3-ITD) negative/NPM1 mutated, biallelic CCAAT/enhancer binding
                            protein alpha (CEBPA) mutation without FLT3-ITD
               -  Chronic myeloid leukemia blast crisis (CML-BC)
                    -  Relapsed or refractory to at least one Bcr-Abl-TKI-containing regimen
               -  Myelodysplastic syndrome (MDS), must meet all of the following:
                    -  Higher risk MDS [intermediate-2 or high risk by the original International
                       Prognostic Scoring System (IPSS)]
                    -  Relapsed, refractory, or intolerant to at least one prior line of therapy
                       containing hypomethylating agents (deoxyribonucleic acid [DNA]
                       methyltransferase inhibitors)
          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 2 (Karnofsky >= 50%)
          -  Total bilirubin =< 1.5 × upper limit of normal (ULN) for the laboratory unless
             resulting from hemolysis
          -  Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
             =< 2.5 × ULN for the laboratory
          -  Creatinine within normal limits for the laboratory OR creatinine clearance >= 60
             mL/min/1.73 m^2 (estimated glomerular filtration rate [eGFR]) for patients with
             creatinine levels above the ULN for the laboratory
          -  Human immunodeficiency virus (HIV)-infected persons are eligible if they meet other
             eligibility criteria including the following:
               -  No prior acquired immune deficiency syndrome (AIDS)-defining condition other than
                  cluster of differentiation (CD)4+ cells nadir < 200/mm^3
               -  Pre-leukemia CD4+ cell count >= 250/mm^3
               -  Willing to adhere to antiretroviral therapy regimen with minimal overlapping
                  toxicity and PK interactions with the experimental agents in this study; no
                  zidovudine- and no ritonavir-containing regimens and no 3-drugs-in-1 pill
                  regimens containing pharmacologic boosters are allowed; recommended regimens are
                  integrase inhibitors combined with tenofovir and emtricitabine
          -  Women of childbearing potential and men must agree to use adequate contraception
             (hormonal or barrier method of birth control; abstinence) prior to study entry, for
             the duration of study participation, and 4 months after completion of AZD1775 and
             belinostat administration
          -  Ability to swallow medication
          -  Ability to understand and the willingness to sign a written informed consent document
        Exclusion Criteria:
          -  Clinical picture indicative of leukostasis or evidence of disseminated intravascular
             coagulopathy
          -  Other investigational agent within 3 weeks prior to initiation of study therapy
          -  Ongoing toxicities >= grade 2 from prior therapy
          -  Acute promyelocytic leukemia (APL, M3)
          -  Active central nervous system (CNS) leukemia
          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to AZD1775 or belinostat
          -  Stem cell transplant within previous 3 months prior to initiation of study therapy
          -  Major surgical procedures =< 28 days before beginning study treatment or minor
             surgical procedures =< 7 day before beginning study treatment; no waiting required
             after placement of a vascular access device
          -  Uncontrolled infection
          -  Pregnant or nursing; women of childbearing potential must have a negative serum
             pregnancy test performed within 7 days prior to the start of study therapy
               -  Note: Pregnant women are excluded from this study; breastfeeding should be
                  discontinued if the mother is treated with AZD1775/belinostat
          -  Circulating blast count >= 50,000/uL within the week preceding enrollment
          -  Current candidacy for a potentially curative allogeneic stem cell transplant, unless
             declined
          -  Corrected QT (QTc) interval >= 450 ms (ie, grade 1 or higher) on electrocardiogram
             (ECG) prior to initiation of study treatment
               -  If baseline QTc on screening ECG is >= 450 ms (ie, grade 1 or higher):
                    -  Check potassium and magnesium serum levels
                    -  Correct any identified hypokalemia and/or hypomagnesemia and repeat ECG to
                       confirm QTc interval
               -  For patients with baseline heart rate (HR) < 60 beats per minute (bpm) or > 100
                  bpm, manual measurement of QT interval by cardiologist is required, with
                  Fridericia correction applied to that manual measurement to determine the QTc for
                  eligibility consideration
               -  Note: For patients with HR 60-100 bpm, manual measurement of QTc interval and use
                  of Fridericia calculation is NOT required
          -  Any of the following related to risk of torsades de pointes and sudden cardiac death:
               -  History of sustained ventricular tachycardia (VT), ventricular fibrillation (VF),
                  torsades de pointes, or resuscitated cardiac arrest unless currently addressed
                  with an implanted cardiac defibrillator
               -  Concomitant treatment with an anti-arrhythmic agent to prevent or control
                  arrhythmia; agents used for rate-control of atrial fibrillation are permitted
                  provided that they are not prohibited due to potential drug interactions
               -  Known congenital long QT syndrome
               -  Second degree atrioventricular (AV) block type II, third degree AV block, or
                  ventricular rate < 50 bpm or > 120 bpm
          -  Unstable angina, myocardial infarction or New York Heart Association (NYHA) class
             III/IV congestive heart failure within 30 days preceding study enrollment
          -  Ongoing or planned treatment with any of the following:
               -  Atorvastatin
               -  Strong inhibitors or inducers of cytochrome P450 family 3, subfamily A,
                  polypeptide 4 (CYP3A4); as part of the enrollment/informed consent procedures,
                  the patient will be counseled on the risk of interactions with other agents, and
                  what to do if new medications need to be prescribed or if the patient is
                  considering a new over-the-counter medicine or herbal product
                    -  If any of these agents have been used, patients must be off them for >= 2
                       weeks before starting study treatment
          -  Any known UGT1A polymorphism, heterozygous or homozygous
          -  History of prior therapy with belinostat or AZD1775
          -  Active gastrointestinal (GI) conditions that might predispose to drug intolerance or
             poor drug absorption
          -  Receiving any other therapies for cancer treatment (with the exception of
             gonadotropin-releasing hormone [GnRH] agonists for prostate cancer); Note: hydroxyurea
             is allowed before initiation of study treatment and for the first 5 days of study
             treatment
          -  Diagnosis or treatment for another malignancy within 3 years of enrollment, with the
             exception of complete resection of basal cell carcinoma or squamous cell carcinoma of
             the skin, any in situ malignancy, or low-risk prostate cancer after curative therapy
          -  Medical, psychological, or social condition that, in the opinion of the investigator,
             may increase the patient's risk, interfere with the patient's participation in the
             study, or hinder evaluation of study results